Abstract This study intends to introduce kernel mean embedding of probability measures over infinite‐dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of probability measures in small open neighborhoods, which identifies a pseudo‐likelihood and fosters a rich framework for statistical inference. Utilizing Maximum Mean Discrepancy, we devise new tests in functional response models. The performance of new derived tests is evaluated against competitors in three major problems in functional data analysis including function‐on‐scalar regression, functional one‐way ANOVA, and equality of covariance operators. This article is protected by copyright. All rights reserved.
{"title":"Kernel Mean Embedding of Probability Measures and its Applications to Functional Data Analysis","authors":"Saeed Hayati, Kenji Fukumizu, Afshin Parvardeh","doi":"10.1111/sjos.12691","DOIUrl":"https://doi.org/10.1111/sjos.12691","url":null,"abstract":"Abstract This study intends to introduce kernel mean embedding of probability measures over infinite‐dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of probability measures in small open neighborhoods, which identifies a pseudo‐likelihood and fosters a rich framework for statistical inference. Utilizing Maximum Mean Discrepancy, we devise new tests in functional response models. The performance of new derived tests is evaluated against competitors in three major problems in functional data analysis including function‐on‐scalar regression, functional one‐way ANOVA, and equality of covariance operators. This article is protected by copyright. All rights reserved.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135923550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and longitudinal data. Envelope methods have been proposed to improve the estimation efficiency in unconstrained multivariate linear models, but have not yet been developed for constrained models. We pursue that development in this article. We first compare the standard envelope estimator with the standard estimator arising from a constrained multivariate model in terms of bias and efficiency. To further improve efficiency, we propose a novel envelope estimator based on a constrained multivariate model. We show the advantage of our proposals by simulations and by studying the probiotic capacity to reduced Salmonella infection. This article is protected by copyright. All rights reserved.
{"title":"Envelopes for multivariate linear regression with linearly constrained coefficients","authors":"Dennis Cook, Liliana Forzani, Lan Liu","doi":"10.1111/sjos.12690","DOIUrl":"https://doi.org/10.1111/sjos.12690","url":null,"abstract":"Abstract A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and longitudinal data. Envelope methods have been proposed to improve the estimation efficiency in unconstrained multivariate linear models, but have not yet been developed for constrained models. We pursue that development in this article. We first compare the standard envelope estimator with the standard estimator arising from a constrained multivariate model in terms of bias and efficiency. To further improve efficiency, we propose a novel envelope estimator based on a constrained multivariate model. We show the advantage of our proposals by simulations and by studying the probiotic capacity to reduced Salmonella infection. This article is protected by copyright. All rights reserved.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135923147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We consider the problem of clustering functional data according to their covariance structure. We contribute a soft clustering methodology based on the Wasserstein‐Procrustes distance, where the in‐between cluster variability is penalised by a term proportional to the entropy of the partition matrix. In this way, each covariance operator can be partially classified into more than one group. Such soft classification allows for clusters to overlap, and arises naturally in situations where the separation between all or some of the clusters is not well‐defined. We also discuss how to estimate the number of groups and to test for the presence of any cluster structure. The algorithm is illustrated using simulated and real data. An R implementation is available in the Supplementary materials. This article is protected by copyright. All rights reserved.
{"title":"Covariance‐based soft clustering of functional data based on the Wasserstein‐Procrustes metric","authors":"Valentina Masarotto, Guido Masarotto","doi":"10.1111/sjos.12692","DOIUrl":"https://doi.org/10.1111/sjos.12692","url":null,"abstract":"Abstract We consider the problem of clustering functional data according to their covariance structure. We contribute a soft clustering methodology based on the Wasserstein‐Procrustes distance, where the in‐between cluster variability is penalised by a term proportional to the entropy of the partition matrix. In this way, each covariance operator can be partially classified into more than one group. Such soft classification allows for clusters to overlap, and arises naturally in situations where the separation between all or some of the clusters is not well‐defined. We also discuss how to estimate the number of groups and to test for the presence of any cluster structure. The algorithm is illustrated using simulated and real data. An R implementation is available in the Supplementary materials. This article is protected by copyright. All rights reserved.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135482582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Greenland, S. (2023). Divergence vs. decision P‐values: A distinction worth making in theory and keeping in practice. <i>Scandinavian Journal of Statistics</i>, 50, 1–35, https://onlinelibrary.wiley.com/doi/10.1111/sjos.12625","authors":"","doi":"10.1111/sjos.12687","DOIUrl":"https://doi.org/10.1111/sjos.12687","url":null,"abstract":"","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135744625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We address the problem of estimating the mixing time of a Markov chain from a single trajectory of observations. Unlike most previous works which employed Hilbert space methods to estimate spectral gaps, we opt for an approach based on contraction with respect to total variation. Specifically, we estimate the contraction coefficient introduced in Wolfer (2020), inspired from Dobrushin's. This quantity, unlike the spectral gap, controls the mixing time up to strong universal constants and remains applicable to nonreversible chains. We improve existing fully data‐dependent confidence intervals around this contraction coefficient, which are both easier to compute and thinner than spectral counterparts. Furthermore, we introduce a novel analysis beyond the worst‐case scenario by leveraging additional information about the transition matrix. This allows us to derive instance‐dependent rates for estimating the matrix with respect to the induced uniform norm, and some of its mixing properties.
{"title":"Empirical and Instance–Dependent Estimation of Markov Chain and Mixing Time","authors":"Geoffrey Wolfer","doi":"10.1111/sjos.12686","DOIUrl":"https://doi.org/10.1111/sjos.12686","url":null,"abstract":"Abstract We address the problem of estimating the mixing time of a Markov chain from a single trajectory of observations. Unlike most previous works which employed Hilbert space methods to estimate spectral gaps, we opt for an approach based on contraction with respect to total variation. Specifically, we estimate the contraction coefficient introduced in Wolfer (2020), inspired from Dobrushin's. This quantity, unlike the spectral gap, controls the mixing time up to strong universal constants and remains applicable to nonreversible chains. We improve existing fully data‐dependent confidence intervals around this contraction coefficient, which are both easier to compute and thinner than spectral counterparts. Furthermore, we introduce a novel analysis beyond the worst‐case scenario by leveraging additional information about the transition matrix. This allows us to derive instance‐dependent rates for estimating the matrix with respect to the induced uniform norm, and some of its mixing properties.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135790340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we construct an approximation to the Pitman–Yor process by truncating its two‐parameter Poisson–Dirichlet representation. The truncation is based on a decreasing sequence of random weights, thus having a lower approximation error compared to the popular truncated stick‐breaking process. We develop an exact simulation algorithm to sample from the approximation process and provide an alternative MCMC algorithm for the parameter regime where the exact simulation algorithm becomes slow. The effectiveness of the simulation algorithms is demonstrated by the estimation of the functionals of a Pitman–Yor process. Then we adapt the approximation process into a Pitman–Yor process mixture model and devise a blocked Gibbs sampler for posterior inference.
{"title":"Truncated two‐parameter <scp>Poisson‐Dirichlet</scp> approximation for <scp>Pitman‐Yor</scp> process hierarchical models","authors":"Junyi Zhang, Angelos Dassios","doi":"10.1111/sjos.12688","DOIUrl":"https://doi.org/10.1111/sjos.12688","url":null,"abstract":"Abstract In this paper, we construct an approximation to the Pitman–Yor process by truncating its two‐parameter Poisson–Dirichlet representation. The truncation is based on a decreasing sequence of random weights, thus having a lower approximation error compared to the popular truncated stick‐breaking process. We develop an exact simulation algorithm to sample from the approximation process and provide an alternative MCMC algorithm for the parameter regime where the exact simulation algorithm becomes slow. The effectiveness of the simulation algorithms is demonstrated by the estimation of the functionals of a Pitman–Yor process. Then we adapt the approximation process into a Pitman–Yor process mixture model and devise a blocked Gibbs sampler for posterior inference.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a novel marginal additive model (MAM) for modelling cluster‐correlated data with non‐linear population‐averaged associations. The proposed MAM is a unified framework for estimation and uncertainty quantification of a marginal mean model, combined with inference for between‐cluster variability and cluster‐specific prediction. We propose a fitting algorithm that enables efficient computation of standard errors and corrects for estimation of penalty terms. We demonstrate the proposed methods in simulations and in application to (i) a longitudinal study of beaver foraging behaviour, and (ii) a spatial analysis of Loaloa infection in West Africa.This article is protected by copyright. All rights reserved.
{"title":"Marginal additive models for population‐averaged inference in longitudinal and cluster‐correlated data","authors":"Glen Mcgee, Alex Stringer","doi":"10.1111/sjos.12681","DOIUrl":"https://doi.org/10.1111/sjos.12681","url":null,"abstract":"We propose a novel marginal additive model (MAM) for modelling cluster‐correlated data with non‐linear population‐averaged associations. The proposed MAM is a unified framework for estimation and uncertainty quantification of a marginal mean model, combined with inference for between‐cluster variability and cluster‐specific prediction. We propose a fitting algorithm that enables efficient computation of standard errors and corrects for estimation of penalty terms. We demonstrate the proposed methods in simulations and in application to (i) a longitudinal study of beaver foraging behaviour, and (ii) a spatial analysis of Loaloa infection in West Africa.This article is protected by copyright. All rights reserved.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45849574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The statistical design for order‐of‐addition (OofA) experiments has received much recent interest as its potential in determining the optimal sequence of multiple components, for example, the optimal sequence of drug administration for disease treatment. The traditional OofA experiments focus mainly on the sequence effects of components, i.e., the experimenters fix the factor level of each component and observe how the response is affected by varying the sequences of components. However, the components may also have factorial effects in that changing their factor levels in a given sequence can affect the response. In view of this, we consider the design problem for OofA experiments where each component is experimented at two levels. A systematic method is given to construct OofA designs that jointly considers the sequence design and factorial design for all components. By appropriately choosing the sequence and factorial designs, we show that the combination of the two parts results in a balanced design with an economical run size. Moreover, the constructed designs enjoy a number of optimality properties such as D‐, A‐ and E‐optimalities under some empirical models. The design method proposed can be extended to some other practical situations like the number of process variables is different from the number of components, and OofA experiments with multi‐level components.This article is protected by copyright. All rights reserved.
{"title":"Design for order‐of‐addition experiments with two‐level components","authors":"Hengzhen Huang","doi":"10.1111/sjos.12678","DOIUrl":"https://doi.org/10.1111/sjos.12678","url":null,"abstract":"The statistical design for order‐of‐addition (OofA) experiments has received much recent interest as its potential in determining the optimal sequence of multiple components, for example, the optimal sequence of drug administration for disease treatment. The traditional OofA experiments focus mainly on the sequence effects of components, i.e., the experimenters fix the factor level of each component and observe how the response is affected by varying the sequences of components. However, the components may also have factorial effects in that changing their factor levels in a given sequence can affect the response. In view of this, we consider the design problem for OofA experiments where each component is experimented at two levels. A systematic method is given to construct OofA designs that jointly considers the sequence design and factorial design for all components. By appropriately choosing the sequence and factorial designs, we show that the combination of the two parts results in a balanced design with an economical run size. Moreover, the constructed designs enjoy a number of optimality properties such as D‐, A‐ and E‐optimalities under some empirical models. The design method proposed can be extended to some other practical situations like the number of process variables is different from the number of components, and OofA experiments with multi‐level components.This article is protected by copyright. All rights reserved.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45017438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In statistical modelling, it is important to know the mechanisms that cause underdispersion. Several mechanisms that lead to underdispersed count distributions are revisited from new perspectives, and new ones are introduced. These include procedures based on the number of arrivals in arrival processes, such as renewal and pure birth processes and steady‐state distributions of birth‐death processes, like queues with state‐dependent service rates. Weighted Poisson and other well‐known underdispersed distributions are also related to birth‐death processes. Classical and variable binomial thinning mechanisms are also viewed as important procedures for generating underdispersed distributions, which can also generate bivariate count distributions with negative correlation. Some example applications are shown, one of which is related to Biodosimetry.This article is protected by copyright. All rights reserved.
{"title":"Some mechanisms leading to underdispersion: old and new proposals","authors":"P. Puig, J. Valero, Amanda Fernández-Fontelo","doi":"10.1111/sjos.12677","DOIUrl":"https://doi.org/10.1111/sjos.12677","url":null,"abstract":"In statistical modelling, it is important to know the mechanisms that cause underdispersion. Several mechanisms that lead to underdispersed count distributions are revisited from new perspectives, and new ones are introduced. These include procedures based on the number of arrivals in arrival processes, such as renewal and pure birth processes and steady‐state distributions of birth‐death processes, like queues with state‐dependent service rates. Weighted Poisson and other well‐known underdispersed distributions are also related to birth‐death processes. Classical and variable binomial thinning mechanisms are also viewed as important procedures for generating underdispersed distributions, which can also generate bivariate count distributions with negative correlation. Some example applications are shown, one of which is related to Biodosimetry.This article is protected by copyright. All rights reserved.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48379896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Lp‐quantile regression generalizes both quantile regression and expectile regression, and has become popular for its robustness and effectiveness especially when 1 < p ≤ 2. In this paper, we consider the data that are inherently distributed and propose two distributed Lp‐quantile regression estimators for a preconceived low‐dimensional parameter in the presence of high‐dimensional extraneous covariates. To handle the impact of high‐dimensional nuisance parameters, we first investigate regularized projection score for estimating low‐dimensional parameter of main interest in Lp‐quantile regression. To deal with the distributed data, we further propose two communication‐efficient surrogate projection score estimators and establish their theoretical properties. The finite‐sample performance of the proposed estimators is studied through simulations and an application to Communities and Crime data set is also presented.This article is protected by copyright. All rights reserved.
Lp‐分位数回归概括了分位数回归和期望回归，并因其稳健性和有效性而广受欢迎，尤其是当1
{"title":"Communication‐efficient low‐dimensional parameter estimation and inference for high‐dimensional Lp‐quantile regression","authors":"Junzhuo Gao, Lei Wang","doi":"10.1111/sjos.12683","DOIUrl":"https://doi.org/10.1111/sjos.12683","url":null,"abstract":"The Lp‐quantile regression generalizes both quantile regression and expectile regression, and has become popular for its robustness and effectiveness especially when 1 < p ≤ 2. In this paper, we consider the data that are inherently distributed and propose two distributed Lp‐quantile regression estimators for a preconceived low‐dimensional parameter in the presence of high‐dimensional extraneous covariates. To handle the impact of high‐dimensional nuisance parameters, we first investigate regularized projection score for estimating low‐dimensional parameter of main interest in Lp‐quantile regression. To deal with the distributed data, we further propose two communication‐efficient surrogate projection score estimators and establish their theoretical properties. The finite‐sample performance of the proposed estimators is studied through simulations and an application to Communities and Crime data set is also presented.This article is protected by copyright. All rights reserved.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42431991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：