Pub Date : 2025-09-25DOI: 10.1016/j.spasta.2025.100928
Yangha Chung , Ji Meng Loh , Woncheol Jang
We introduce a doubly-smoothed bandwidth selection method to obtain bandwidth matrices for estimating the intensity function of a spatial point process. The doubly-smoothed bootstrap involves taking bootstrap samples by adding random noise and using Dirichlet rather than multinomial weights. The mean integrated squared error (MISE) and asymptotic mean integrated squared error (AMISE) as a function of can then be computed numerically using the bootstrap samples, with optimal obtained by minimizing the MISE or AMISE with respect to We present simulation results comparing the doubly-smoothed bandwidth selection method with other methods for a number of intensity functions. We also apply our methods to a data set of police pedestrian stops in New York City.
{"title":"Bandwidth selection for the intensity in spatial point processes","authors":"Yangha Chung , Ji Meng Loh , Woncheol Jang","doi":"10.1016/j.spasta.2025.100928","DOIUrl":"10.1016/j.spasta.2025.100928","url":null,"abstract":"<div><div>We introduce a doubly-smoothed bandwidth selection method to obtain bandwidth matrices <span><math><mi>H</mi></math></span> for estimating the intensity function of a spatial point process. The doubly-smoothed bootstrap involves taking bootstrap samples by adding random noise and using Dirichlet rather than multinomial weights. The mean integrated squared error (MISE) and asymptotic mean integrated squared error (AMISE) as a function of <span><math><mi>H</mi></math></span> can then be computed numerically using the bootstrap samples, with optimal <span><math><mi>H</mi></math></span> obtained by minimizing the MISE or AMISE with respect to <span><math><mrow><mi>H</mi><mo>.</mo></mrow></math></span> We present simulation results comparing the doubly-smoothed bandwidth selection method with other methods for a number of intensity functions. We also apply our methods to a data set of police pedestrian stops in New York City.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100928"},"PeriodicalIF":2.5,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-24DOI: 10.1016/j.spasta.2025.100933
Maria E. Kamenetsky , Jun Zhu , Ronald E. Gangnon
Patterns in disease across space and time are important to epidemiologists and health professionals because they may indicate underlying elevated disease risk. In some cases, elevated risk may be driven by environmental exposures, infectious diseases or other factors where timely public health interventions are important. The spatial and spatio-temporal scan statistics identify a single most likely cluster or equivalently select a single correct model. We instead consider an ensemble of single cluster models. We use stacking, a model-averaging technique, to combine relative risk estimates from all of the single cluster models into a sequence of meta-models indexed by the effective number of parameters/clusters. The number of parameters/spatio-temporal clusters is chosen using information criteria. A simulation study is conducted to demonstrate the statistical properties of the stacking method. The method is illustrated using a dataset of female breast cancer incidence data at the municipality level in Japan.
{"title":"Spatial and spatio-temporal cluster detection using stacking","authors":"Maria E. Kamenetsky , Jun Zhu , Ronald E. Gangnon","doi":"10.1016/j.spasta.2025.100933","DOIUrl":"10.1016/j.spasta.2025.100933","url":null,"abstract":"<div><div>Patterns in disease across space and time are important to epidemiologists and health professionals because they may indicate underlying elevated disease risk. In some cases, elevated risk may be driven by environmental exposures, infectious diseases or other factors where timely public health interventions are important. The spatial and spatio-temporal scan statistics identify a single most likely cluster or equivalently select a single correct model. We instead consider an ensemble of single cluster models. We use stacking, a model-averaging technique, to combine relative risk estimates from all of the single cluster models into a sequence of meta-models indexed by the effective number of parameters/clusters. The number of parameters/spatio-temporal clusters is chosen using information criteria. A simulation study is conducted to demonstrate the statistical properties of the stacking method. The method is illustrated using a dataset of female breast cancer incidence data at the municipality level in Japan.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100933"},"PeriodicalIF":2.5,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-23DOI: 10.1016/j.spasta.2025.100934
Giovanni Millo
We address the issue of specifying a spatial lag vs. spatial error process in spatial panel models. The popular locally robust Lagrange multiplier (RLM) tests for spatial lag vs. error are compared to optimal alternatives based on maximum likelihood estimation: Wald and likelihood ratio (LR) tests requiring estimation of the full encompassing model, and conditional Lagrange multiplier (CLM) tests drawing on the reduced specification. Monte Carlo simulations are performed in a typical spatial panel context. Individual effects are successfully eliminated through the forward orthogonal deviations transformation, making the RLM suitable for panel data. Nevertheless, the statistical properties of Wald and LR are superior to those of the RLM. The CLM also dominates the RLM, as long as the sample is at least of moderate size. The RLM are computationally very convenient, but ML-based tests are feasible in most usage cases on mainstream hardware.
{"title":"Specifying spatial effects in panel data: Locally robust vs. conditional tests","authors":"Giovanni Millo","doi":"10.1016/j.spasta.2025.100934","DOIUrl":"10.1016/j.spasta.2025.100934","url":null,"abstract":"<div><div>We address the issue of specifying a spatial lag vs. spatial error process in spatial panel models. The popular locally robust Lagrange multiplier (RLM) tests for spatial lag vs. error are compared to optimal alternatives based on maximum likelihood estimation: Wald and likelihood ratio (LR) tests requiring estimation of the full encompassing model, and conditional Lagrange multiplier (CLM) tests drawing on the reduced specification. Monte Carlo simulations are performed in a typical spatial panel context. Individual effects are successfully eliminated through the forward orthogonal deviations transformation, making the RLM suitable for panel data. Nevertheless, the statistical properties of Wald and LR are superior to those of the RLM. The CLM also dominates the RLM, as long as the sample is at least of moderate size. The RLM are computationally very convenient, but ML-based tests are feasible in most usage cases on mainstream hardware.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100934"},"PeriodicalIF":2.5,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-23DOI: 10.1016/j.spasta.2025.100931
Aibing Ji, Jingxuan Li, Qingqing Li
The spatial autoregressive panel data models are widely employed in regional economics to capture spatial dependencies, but conventional specifications rely on a single spatial weight matrix, heightening the risk of model misspecification. Current research lacks systematic model averaging methods for integrating multiple weight matrices and addressing spatial effect uncertainty. This study proposes a novel model averaging framework for spatial autoregressive panel data models with fixed effects, extending model averaging methodology to the spatial panel context and enabling flexible combinations of multiple weight matrices for both dependent variables and error terms. An adaptive Mallows-type criterion is developed, dynamically adjusting to the presence or absence of spatial effects, with its asymptotic optimality established. Monte Carlo simulations confirm robustness across scenarios with no, single, or mixed spatial dependencies. An empirical application to Chinese provincial housing prices identifies economic adjacency as the key spatial dependence driver, validating the method’s predictive accuracy and policy utility for spatiotemporal data analysis.
{"title":"Model averaging for spatial autoregressive panel data models","authors":"Aibing Ji, Jingxuan Li, Qingqing Li","doi":"10.1016/j.spasta.2025.100931","DOIUrl":"10.1016/j.spasta.2025.100931","url":null,"abstract":"<div><div>The spatial autoregressive panel data models are widely employed in regional economics to capture spatial dependencies, but conventional specifications rely on a single spatial weight matrix, heightening the risk of model misspecification. Current research lacks systematic model averaging methods for integrating multiple weight matrices and addressing spatial effect uncertainty. This study proposes a novel model averaging framework for spatial autoregressive panel data models with fixed effects, extending model averaging methodology to the spatial panel context and enabling flexible combinations of multiple weight matrices for both dependent variables and error terms. An adaptive Mallows-type criterion is developed, dynamically adjusting to the presence or absence of spatial effects, with its asymptotic optimality established. Monte Carlo simulations confirm robustness across scenarios with no, single, or mixed spatial dependencies. An empirical application to Chinese provincial housing prices identifies economic adjacency as the key spatial dependence driver, validating the method’s predictive accuracy and policy utility for spatiotemporal data analysis.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100931"},"PeriodicalIF":2.5,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-22DOI: 10.1016/j.spasta.2025.100932
Jinsheng Xie
This study aims to establish uncertain spatial statistics by exploring the uncertain spatial autoregressive model firstly. Modeling the observations of the response variable via uncertain variables and assuming they are affected by neighboring observations, this paper explores an approach of the uncertain spatial autoregressive model to estimate relationships among the uncertain variables with spatial locations. By employing the principle of least squares, a minimization problem is provided to estimate unknown parameters in the uncertain spatial autoregressive model. Finally, two real-world examples of regional economic analysis and regional air quality analysis are given to clearly demonstrate the uncertain spatial autoregressive model.
{"title":"Uncertain spatial autoregressive model with applications to regional economic analysis and regional air quality analysis","authors":"Jinsheng Xie","doi":"10.1016/j.spasta.2025.100932","DOIUrl":"10.1016/j.spasta.2025.100932","url":null,"abstract":"<div><div>This study aims to establish uncertain spatial statistics by exploring the uncertain spatial autoregressive model firstly. Modeling the observations of the response variable via uncertain variables and assuming they are affected by neighboring observations, this paper explores an approach of the uncertain spatial autoregressive model to estimate relationships among the uncertain variables with spatial locations. By employing the principle of least squares, a minimization problem is provided to estimate unknown parameters in the uncertain spatial autoregressive model. Finally, two real-world examples of regional economic analysis and regional air quality analysis are given to clearly demonstrate the uncertain spatial autoregressive model.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100932"},"PeriodicalIF":2.5,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-11DOI: 10.1016/j.spasta.2025.100930
Daniela Silva , Raquel Menezes , Gonçalo Araújo , Renato Rosa , Ana Moreno , Alexandra Silva , Susana Garrido
Accurately identifying spatial patterns of species distribution is crucial for scientific insight and societal benefit, aiding our understanding of species fluctuations. The increasing quantity and quality of ecological datasets present heightened statistical challenges, complicating spatial species dynamics comprehension. Addressing the complex task of integrating multiple data sources to enhance spatial fish distribution understanding in marine ecology, this study introduces a pioneering five-layer Joint model. The model adeptly integrates fishery-independent and fishery-dependent data, accommodating zero-inflated data and distinct sampling processes. A comprehensive simulation study evaluates the model performance across various preferential sampling scenarios and sample sizes, elucidating its advantages and challenges. Our findings highlight the model’s robustness in estimating preferential parameters, emphasizing differentiation between presence–absence and biomass observations. Evaluation of estimation of spatial covariance and prediction performance underscores the model’s reliability. Augmenting sample sizes reduces parameter estimation variability, aligning with the principle that increased information enhances certainty. Assessing the contribution of each data source reveals successful integration, providing a comprehensive representation of biomass patterns. Empirical application within a real-world context further solidifies the model’s efficacy in capturing species’ spatial distribution. This research advances methodologies for integrating diverse datasets with different sampling natures further contributing to a more informed understanding of spatial dynamics of marine species.
{"title":"Joint model for zero-inflated data combining fishery-dependent and fishery-independent sources","authors":"Daniela Silva , Raquel Menezes , Gonçalo Araújo , Renato Rosa , Ana Moreno , Alexandra Silva , Susana Garrido","doi":"10.1016/j.spasta.2025.100930","DOIUrl":"10.1016/j.spasta.2025.100930","url":null,"abstract":"<div><div>Accurately identifying spatial patterns of species distribution is crucial for scientific insight and societal benefit, aiding our understanding of species fluctuations. The increasing quantity and quality of ecological datasets present heightened statistical challenges, complicating spatial species dynamics comprehension. Addressing the complex task of integrating multiple data sources to enhance spatial fish distribution understanding in marine ecology, this study introduces a pioneering five-layer Joint model. The model adeptly integrates fishery-independent and fishery-dependent data, accommodating zero-inflated data and distinct sampling processes. A comprehensive simulation study evaluates the model performance across various preferential sampling scenarios and sample sizes, elucidating its advantages and challenges. Our findings highlight the model’s robustness in estimating preferential parameters, emphasizing differentiation between presence–absence and biomass observations. Evaluation of estimation of spatial covariance and prediction performance underscores the model’s reliability. Augmenting sample sizes reduces parameter estimation variability, aligning with the principle that increased information enhances certainty. Assessing the contribution of each data source reveals successful integration, providing a comprehensive representation of biomass patterns. Empirical application within a real-world context further solidifies the model’s efficacy in capturing species’ spatial distribution. This research advances methodologies for integrating diverse datasets with different sampling natures further contributing to a more informed understanding of spatial dynamics of marine species.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100930"},"PeriodicalIF":2.5,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145107607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-10DOI: 10.1016/j.spasta.2025.100929
Zhenhua Wang , Paul A. Parker , Scott H. Holan
Small area estimation models are essential for estimating population characteristics in regions with limited sample sizes, thereby supporting policy decisions, demographic studies, and resource allocation, among other use cases. The spatial Fay–Herriot model is one such approach that incorporates spatial dependence to improve estimation by borrowing strength from neighboring regions. However, this approach often requires substantial computational resources, limiting its scalability for high-dimensional datasets, especially when considering multiple (multivariate) responses. This paper proposes two methods that integrate the multivariate spatial Fay–Herriot model with spatial random effects, learned through variational autoencoders, to efficiently leverage spatial structure. Importantly, after training the variational autoencoder to represent spatial dependence for a given set of geographies, it may be used again in future modeling efforts, without the need for retraining. Additionally, the use of the variational autoencoder to represent spatial dependence results in extreme improvements in computational efficiency, even for massive datasets. We demonstrate the effectiveness of our approach using 5-year period estimates from the American Community Survey over all census tracts in California.
{"title":"Variational autoencoded multivariate spatial Fay–Herriot models","authors":"Zhenhua Wang , Paul A. Parker , Scott H. Holan","doi":"10.1016/j.spasta.2025.100929","DOIUrl":"10.1016/j.spasta.2025.100929","url":null,"abstract":"<div><div>Small area estimation models are essential for estimating population characteristics in regions with limited sample sizes, thereby supporting policy decisions, demographic studies, and resource allocation, among other use cases. The spatial Fay–Herriot model is one such approach that incorporates spatial dependence to improve estimation by borrowing strength from neighboring regions. However, this approach often requires substantial computational resources, limiting its scalability for high-dimensional datasets, especially when considering multiple (multivariate) responses. This paper proposes two methods that integrate the multivariate spatial Fay–Herriot model with spatial random effects, learned through variational autoencoders, to efficiently leverage spatial structure. Importantly, after training the variational autoencoder to represent spatial dependence for a given set of geographies, it may be used again in future modeling efforts, without the need for retraining. Additionally, the use of the variational autoencoder to represent spatial dependence results in extreme improvements in computational efficiency, even for massive datasets. We demonstrate the effectiveness of our approach using 5-year period estimates from the American Community Survey over all census tracts in California.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100929"},"PeriodicalIF":2.5,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-26DOI: 10.1016/j.spasta.2025.100927
Giampiero M. Gallo , Demetrio Lacava , Edoardo Otranto
This paper introduces a novel two-stage modeling framework that combines Markov Switching (MS) models with an autoregressive model augmented by spatial effects to analyze the dynamics and spatial interdependence of Biden’s polling percentages during the 2020 electoral campaign. In the first stage, we employ MS models to segment each state’s daily polling time series into distinct regimes — interpreted as phases of decline, stability, and growth. This segmentation captures abrupt changes and local trends in public opinion, enabling us to link regime shifts with key political events such as debates, party conventions, and milestone campaign achievements. The inherent nonlinearity of polling data would otherwise be lost by first differencing. By removing the regime-specific components, we generate stationary residuals modeled using an Autoregressive model with exogenous variables (ARX) that incorporates political spatial interactions through two complementary effects. The spillover effect captures lagged influences arising from politically influential states, while the contagion effect reflects the contemporaneous impact of neighboring states. A recursive algorithm based on partial correlations is implemented to select the most relevant spillover sources for each state. Empirical results, based on daily data from 13 swing states, reveal robust evidence of persistent regime structures and marked spatial dependencies. While contagion effects are uniformly significant across states, spillover dynamics exhibit considerable heterogeneity in both magnitude and direction. This integrated modeling approach enhances our understanding of the complex, nonlinear temporal evolution of polling trends and the spatial diffusion of political opinions that underpinned the 2020 electoral outcome.
{"title":"Regime changes and spatial dependence in the 2020 US presidential election polls","authors":"Giampiero M. Gallo , Demetrio Lacava , Edoardo Otranto","doi":"10.1016/j.spasta.2025.100927","DOIUrl":"10.1016/j.spasta.2025.100927","url":null,"abstract":"<div><div>This paper introduces a novel two-stage modeling framework that combines Markov Switching (MS) models with an autoregressive model augmented by spatial effects to analyze the dynamics and spatial interdependence of Biden’s polling percentages during the 2020 electoral campaign. In the first stage, we employ MS models to segment each state’s daily polling time series into distinct regimes — interpreted as phases of decline, stability, and growth. This segmentation captures abrupt changes and local trends in public opinion, enabling us to link regime shifts with key political events such as debates, party conventions, and milestone campaign achievements. The inherent nonlinearity of polling data would otherwise be lost by first differencing. By removing the regime-specific components, we generate stationary residuals modeled using an Autoregressive model with exogenous variables (ARX) that incorporates political spatial interactions through two complementary effects. The spillover effect captures lagged influences arising from politically influential states, while the contagion effect reflects the contemporaneous impact of neighboring states. A recursive algorithm based on partial correlations is implemented to select the most relevant spillover sources for each state. Empirical results, based on daily data from 13 swing states, reveal robust evidence of persistent regime structures and marked spatial dependencies. While contagion effects are uniformly significant across states, spillover dynamics exhibit considerable heterogeneity in both magnitude and direction. This integrated modeling approach enhances our understanding of the complex, nonlinear temporal evolution of polling trends and the spatial diffusion of political opinions that underpinned the 2020 electoral outcome.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"69 ","pages":"Article 100927"},"PeriodicalIF":2.5,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144909070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-22DOI: 10.1016/j.spasta.2025.100926
Wentao Wang , Dengkui Li
This paper considers spatial autoregressive kink models with an unknown threshold, where the impact of a specific explanatory variable on the response variable is piecewise linear but differs below and above this threshold. To address the endogeneity issue, the paper presents the modified generalized method of moments (GMM) that consistently estimates the threshold location and slope changes. Asymptotic properties, including the consistency and asymptotic normality of the GMM estimators, and the limiting distribution of the Sup-Wald statistic, are established under a set of regularity assumptions. In view of the nonstandard asymptotic null distribution, we use a multiplier bootstrap to approximate the -value of the Sup-Wald statistic to detect the presence of the threshold. Simulation study illustrates that the estimators and inference are well-behaved in finite samples. An empirical application to the secondary industrial structure data of 280 Chinese prefecture-level cities further highlights the practical merits of our methods.
{"title":"GMM inference for the spatial autoregressive kink model with an unknown threshold","authors":"Wentao Wang , Dengkui Li","doi":"10.1016/j.spasta.2025.100926","DOIUrl":"10.1016/j.spasta.2025.100926","url":null,"abstract":"<div><div>This paper considers spatial autoregressive kink models with an unknown threshold, where the impact of a specific explanatory variable on the response variable is piecewise linear but differs below and above this threshold. To address the endogeneity issue, the paper presents the modified generalized method of moments (GMM) that consistently estimates the threshold location and slope changes. Asymptotic properties, including the consistency and asymptotic normality of the GMM estimators, and the limiting distribution of the Sup-Wald statistic, are established under a set of regularity assumptions. In view of the nonstandard asymptotic null distribution, we use a multiplier bootstrap to approximate the <span><math><mi>p</mi></math></span>-value of the Sup-Wald statistic to detect the presence of the threshold. Simulation study illustrates that the estimators and inference are well-behaved in finite samples. An empirical application to the secondary industrial structure data of 280 Chinese prefecture-level cities further highlights the practical merits of our methods.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"69 ","pages":"Article 100926"},"PeriodicalIF":2.5,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144909069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-05DOI: 10.1016/j.spasta.2025.100924
Christophe A.N. Biscio , Adrien Mazoyer , Martin V. Vejling
Monte Carlo tests are widely used for computing valid -values without requiring known distributions of test statistics. When performing multiple Monte Carlo tests, it is essential to maintain control of the type I error. Some techniques for multiplicity control pose requirements on the joint distribution of the -values, for instance independence, which can be computationally intensive to achieve, as it requires simulating disjoint null samples for each test. We refer to this as naïve multiple Monte Carlo testing. We highlight in this work that multiple Monte Carlo testing is an instance of conformal novelty detection. Leveraging this insight enables a more efficient multiple Monte Carlo testing procedure, avoiding excessive simulations by using a single null sample for all the tests, while still ensuring exact control over the false discovery rate or the family-wise error rate. We call this approach conformal multiple Monte Carlo testing. The performance is investigated in the context of global envelope tests for point pattern data through a simulation study and an application to a sweat gland data set. Results reveal that with a fixed simulation budget, our proposed method yields substantial improvements in power of the testing procedure as compared to the naïve multiple Monte Carlo testing procedure.
{"title":"Conformal novelty detection for replicate point patterns with FDR or FWER control","authors":"Christophe A.N. Biscio , Adrien Mazoyer , Martin V. Vejling","doi":"10.1016/j.spasta.2025.100924","DOIUrl":"10.1016/j.spasta.2025.100924","url":null,"abstract":"<div><div>Monte Carlo tests are widely used for computing valid <span><math><mi>p</mi></math></span>-values without requiring known distributions of test statistics. When performing multiple Monte Carlo tests, it is essential to maintain control of the type I error. Some techniques for multiplicity control pose requirements on the joint distribution of the <span><math><mi>p</mi></math></span>-values, for instance independence, which can be computationally intensive to achieve, as it requires simulating disjoint null samples for each test. We refer to this as naïve multiple Monte Carlo testing. We highlight in this work that multiple Monte Carlo testing is an instance of conformal novelty detection. Leveraging this insight enables a more efficient multiple Monte Carlo testing procedure, avoiding excessive simulations by using a single null sample for all the tests, while still ensuring exact control over the false discovery rate or the family-wise error rate. We call this approach conformal multiple Monte Carlo testing. The performance is investigated in the context of global envelope tests for point pattern data through a simulation study and an application to a sweat gland data set. Results reveal that with a fixed simulation budget, our proposed method yields substantial improvements in power of the testing procedure as compared to the naïve multiple Monte Carlo testing procedure.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"69 ","pages":"Article 100924"},"PeriodicalIF":2.5,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144860831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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