Pub Date : 2025-08-20DOI: 10.1016/j.jspi.2025.106335
Katarzyna Filipiak , Dietrich von Rosen , Wojciech Rejchel , Martin Singull
The main goal of this paper is to determine maximum likelihood estimators under a multivariate linear model with prior information introduced via inequality restrictions on the mean parameters. The restrictions are in the form of quadratic inequalities. Methods from convex optimization theory play a fundamental role in determining the estimators. A characteristic of the new estimators, called Safety Belt estimators, is that depending on the observed data, there are two alternative solutions to the likelihood equations.
{"title":"The Safety Belt estimator under multivariate linear models with inequality constraints","authors":"Katarzyna Filipiak , Dietrich von Rosen , Wojciech Rejchel , Martin Singull","doi":"10.1016/j.jspi.2025.106335","DOIUrl":"10.1016/j.jspi.2025.106335","url":null,"abstract":"<div><div>The main goal of this paper is to determine maximum likelihood estimators under a multivariate linear model with prior information introduced via inequality restrictions on the mean parameters. The restrictions are in the form of quadratic inequalities. Methods from convex optimization theory play a fundamental role in determining the estimators. A characteristic of the new estimators, called Safety Belt estimators, is that depending on the observed data, there are two alternative solutions to the likelihood equations.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"241 ","pages":"Article 106335"},"PeriodicalIF":0.8,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144878786","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 this paper, we develop optimal designs for growth curve models with count data based on the Rasch Poisson-Gamma counts model (RPGCM). This model is often used in educational and psychological testing when test results yield count data. In the RPGCM, the test scores are determined by respondents ability and item difficulty. Locally -optimal designs are derived for maximum quasi-likelihood estimation to efficiently estimate the mean abilities of the respondents over time. Using the log link, both unstructured, linear and nonlinear growth curves of log mean abilities are taken into account. Finally, the sensitivity of the derived optimal designs due to an imprecise choice of parameter values is analyzed using -efficiency.
{"title":"Optimal design in repeated testing for count data","authors":"Parisa Parsamaram , Heinz Holling , Rainer Schwabe","doi":"10.1016/j.jspi.2025.106334","DOIUrl":"10.1016/j.jspi.2025.106334","url":null,"abstract":"<div><div>In this paper, we develop optimal designs for growth curve models with count data based on the Rasch Poisson-Gamma counts model (RPGCM). This model is often used in educational and psychological testing when test results yield count data. In the RPGCM, the test scores are determined by respondents ability and item difficulty. Locally <span><math><mi>D</mi></math></span>-optimal designs are derived for maximum quasi-likelihood estimation to efficiently estimate the mean abilities of the respondents over time. Using the log link, both unstructured, linear and nonlinear growth curves of log mean abilities are taken into account. Finally, the sensitivity of the derived optimal designs due to an imprecise choice of parameter values is analyzed using <span><math><mi>D</mi></math></span>-efficiency.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"241 ","pages":"Article 106334"},"PeriodicalIF":0.8,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144866420","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}
Pub Date : 2025-08-13DOI: 10.1016/j.jspi.2025.106332
Natalia Markovich , Maksim Ryzhov , Marijus Vaičiulis
The evolution of random undirected graphs by the clustering attachment (CA) both without node and edge deletion and with uniform node or edge deletion is investigated. Theoretical results are obtained for the CA without node and edge deletion when a newly appended node is connected to two existing nodes of the graph at each evolution step. Theoretical results are the following: (1) the sequence of increments of the consecutive mean clustering coefficients tends to zero; (2) the sequences of node degrees and triangle counts of any fixed node are proved to be submartingales. These results were obtained for any initial graph. The simulation study is provided for the CA with uniform node or edge deletion and without any deletion. It is shown that (1) the CA leads to light-tailed distributed node degrees and triangle counts; (2) the average clustering coefficient tends to a constant over time; (3) the mean node degree and the mean triangle count increase over time with the rate depending on the parameters of the CA. The exposition is accompanied by a real data study.
{"title":"Inferences for random graphs evolved by clustering attachment","authors":"Natalia Markovich , Maksim Ryzhov , Marijus Vaičiulis","doi":"10.1016/j.jspi.2025.106332","DOIUrl":"10.1016/j.jspi.2025.106332","url":null,"abstract":"<div><div>The evolution of random undirected graphs by the clustering attachment (CA) both without node and edge deletion and with uniform node or edge deletion is investigated. Theoretical results are obtained for the CA without node and edge deletion when a newly appended node is connected to two existing nodes of the graph at each evolution step. Theoretical results are the following: (1) the sequence of increments of the consecutive mean clustering coefficients tends to zero; (2) the sequences of node degrees and triangle counts of any fixed node are proved to be submartingales. These results were obtained for any initial graph. The simulation study is provided for the CA with uniform node or edge deletion and without any deletion. It is shown that (1) the CA leads to light-tailed distributed node degrees and triangle counts; (2) the average clustering coefficient tends to a constant over time; (3) the mean node degree and the mean triangle count increase over time with the rate depending on the parameters of the CA. The exposition is accompanied by a real data study.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"241 ","pages":"Article 106332"},"PeriodicalIF":0.8,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144851991","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}
Pub Date : 2025-08-09DOI: 10.1016/j.jspi.2025.106333
Yozo Tonaki , Yusuke Kaino , Masayuki Uchida
We consider parametric estimation for a second order linear parabolic stochastic partial differential equation (SPDE) in two space dimensions driven by a -Wiener process with a small noise based on high frequency spatio-temporal data. We first provide estimators of the diffusive and advective parameters in the SPDE using temporal and spatial increments. We then construct an estimator of the reaction parameter in the SPDE based on an approximate coordinate process. We also give simulation results of the proposed estimators.
{"title":"Small dispersion asymptotics for an SPDE in two space dimensions using triple increments","authors":"Yozo Tonaki , Yusuke Kaino , Masayuki Uchida","doi":"10.1016/j.jspi.2025.106333","DOIUrl":"10.1016/j.jspi.2025.106333","url":null,"abstract":"<div><div>We consider parametric estimation for a second order linear parabolic stochastic partial differential equation (SPDE) in two space dimensions driven by a <span><math><mi>Q</mi></math></span>-Wiener process with a small noise based on high frequency spatio-temporal data. We first provide estimators of the diffusive and advective parameters in the SPDE using temporal and spatial increments. We then construct an estimator of the reaction parameter in the SPDE based on an approximate coordinate process. We also give simulation results of the proposed estimators.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"241 ","pages":"Article 106333"},"PeriodicalIF":0.8,"publicationDate":"2025-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144851992","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}
Pub Date : 2025-07-28DOI: 10.1016/j.jspi.2025.106326
Xirui Liu , Ke Yang , Liwen Xu , Mixia Wu
This paper investigates data distributed across various machines in a non-random manner. We introduce two innovative distributed estimators, tailored to accommodate varying levels of communication cost and data privacy protection. The proposed estimators adeptly addresses the challenges associated with the non-random distribution of data. Both methods are communication-efficient, necessitating only two rounds of communication between the Master and worker machines, and safeguard data privacy by solely sharing summary statistics. Under mild conditions, we establish the -error bound and the asymptotic distribution of the estimators. Theoretical analysis confirms that the proposed estimators are statistically efficient. Additionally, numerical simulations and two real-world applications demonstrate the good performance of the proposed methods.
{"title":"Privacy-preserving estimation for non-randomly distributed data","authors":"Xirui Liu , Ke Yang , Liwen Xu , Mixia Wu","doi":"10.1016/j.jspi.2025.106326","DOIUrl":"10.1016/j.jspi.2025.106326","url":null,"abstract":"<div><div>This paper investigates data distributed across various machines in a non-random manner. We introduce two innovative distributed estimators, tailored to accommodate varying levels of communication cost and data privacy protection. The proposed estimators adeptly addresses the challenges associated with the non-random distribution of data. Both methods are communication-efficient, necessitating only two rounds of communication between the Master and worker machines, and safeguard data privacy by solely sharing summary statistics. Under mild conditions, we establish the <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-error bound and the asymptotic distribution of the estimators. Theoretical analysis confirms that the proposed estimators are statistically efficient. Additionally, numerical simulations and two real-world applications demonstrate the good performance of the proposed methods.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"241 ","pages":"Article 106326"},"PeriodicalIF":0.8,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144771447","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}
Pub Date : 2025-07-23DOI: 10.1016/j.jspi.2025.106325
Ming-Chung Chang , Jing-Wen Huang , Frederick Kin Hing Phoa
Experiments involving connected units are prevalent across various scientific disciplines. In such settings, an experimental unit may interact with others, leading to potential contamination effects, referred to in this study as network adjustments, which influence the responses of neighboring units. This paper addresses the design problem for connected experimental units subjected to unstructured treatments under linear models, explicitly incorporating network adjustments to account for correlated responses. We employ alphabetic optimality criteria to identify efficient designs that enhance the precision of treatment effect estimation and the accuracy of quantifying network adjustments. Theoretical conditions and practical guidelines for optimal designs are developed and validated through numerical simulations and application to a real-world network. Our findings demonstrate that the proposed approach delivers highly efficient designs while maintaining low computational complexity.
{"title":"Optimal designs for network experimentation with unstructured treatments","authors":"Ming-Chung Chang , Jing-Wen Huang , Frederick Kin Hing Phoa","doi":"10.1016/j.jspi.2025.106325","DOIUrl":"10.1016/j.jspi.2025.106325","url":null,"abstract":"<div><div>Experiments involving connected units are prevalent across various scientific disciplines. In such settings, an experimental unit may interact with others, leading to potential contamination effects, referred to in this study as <em>network adjustments</em>, which influence the responses of neighboring units. This paper addresses the design problem for connected experimental units subjected to unstructured treatments under linear models, explicitly incorporating network adjustments to account for correlated responses. We employ alphabetic optimality criteria to identify efficient designs that enhance the precision of treatment effect estimation and the accuracy of quantifying network adjustments. Theoretical conditions and practical guidelines for optimal designs are developed and validated through numerical simulations and application to a real-world network. Our findings demonstrate that the proposed approach delivers highly efficient designs while maintaining low computational complexity.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"241 ","pages":"Article 106325"},"PeriodicalIF":0.8,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766436","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}
Pub Date : 2025-07-22DOI: 10.1016/j.jspi.2025.106327
Ingrid Dæhlen , Nils Lid Hjort
This article concerns hybrid combinations of empirical and parametric likelihood functions. Combining the two allows classical parametric likelihood to be crucially modified via the nonparametric counterpart, making possible model misspecification less problematic. Limit theory for the hybrid likelihood function is sorted out, also outside of the parametric model conditions. We prove a profiling result as well as limiting behaviour of the maximizer of the hybrid likelihood function. Our results allow for the presence of plug-in parameters in the hybrid and empirical likelihood framework. Furthermore, the variance and mean squared error of these estimators are studied, with recipes for their estimation. The latter is used to define a focused information criterion, which can be used to choose how the parametric and empirical part of the hybrid combination should be balanced. This allows for hybrid models to be fitted in a context driven way.
{"title":"Model robust hybrid likelihood","authors":"Ingrid Dæhlen , Nils Lid Hjort","doi":"10.1016/j.jspi.2025.106327","DOIUrl":"10.1016/j.jspi.2025.106327","url":null,"abstract":"<div><div>This article concerns hybrid combinations of empirical and parametric likelihood functions. Combining the two allows classical parametric likelihood to be crucially modified via the nonparametric counterpart, making possible model misspecification less problematic. Limit theory for the hybrid likelihood function is sorted out, also outside of the parametric model conditions. We prove a profiling result as well as limiting behaviour of the maximizer of the hybrid likelihood function. Our results allow for the presence of plug-in parameters in the hybrid and empirical likelihood framework. Furthermore, the variance and mean squared error of these estimators are studied, with recipes for their estimation. The latter is used to define a focused information criterion, which can be used to choose how the parametric and empirical part of the hybrid combination should be balanced. This allows for hybrid models to be fitted in a context driven way.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"241 ","pages":"Article 106327"},"PeriodicalIF":0.8,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144723908","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}
Pub Date : 2025-07-11DOI: 10.1016/j.jspi.2025.106311
Phillip B. Mogensen, Bo Markussen
Hypothesis testing is a key part of empirical science and multiple testing as well as the combination of evidence from several tests are continued areas of research. In this article we consider the problem of combining the results of multiple hypothesis tests to (i) test global hypotheses and (ii) make marginal inference while controlling the -FWER. We propose a new family of combination tests for joint hypotheses, called the ‘Too Many, Too Improbable’ (TMTI) statistics, which we show through simulation to have higher power than other combination tests against many alternatives. Furthermore, we prove that a large family of combination tests – which includes the one we propose but also other combination tests – admits a quadratic shortcut when used in a Closed Testing Procedure, which controls the FWER strongly. We develop an algorithm that is linear in the number of hypotheses for obtaining confidence sets for the number of false hypotheses among a collection of hypotheses and an algorithm that is cubic in the number of hypotheses for controlling the -FWER for any greater than one.
{"title":"Too Many, Too Improbable: Testing joint hypotheses and closed testing shortcuts","authors":"Phillip B. Mogensen, Bo Markussen","doi":"10.1016/j.jspi.2025.106311","DOIUrl":"10.1016/j.jspi.2025.106311","url":null,"abstract":"<div><div>Hypothesis testing is a key part of empirical science and multiple testing as well as the combination of evidence from several tests are continued areas of research. In this article we consider the problem of combining the results of multiple hypothesis tests to (i) test global hypotheses and (ii) make marginal inference while controlling the <span><math><mi>k</mi></math></span>-FWER. We propose a new family of combination tests for joint hypotheses, called the ‘Too Many, Too Improbable’ (TMTI) statistics, which we show through simulation to have higher power than other combination tests against many alternatives. Furthermore, we prove that a large family of combination tests – which includes the one we propose but also other combination tests – admits a quadratic shortcut when used in a Closed Testing Procedure, which controls the FWER strongly. We develop an algorithm that is linear in the number of hypotheses for obtaining confidence sets for the number of false hypotheses among a collection of hypotheses and an algorithm that is cubic in the number of hypotheses for controlling the <span><math><mi>k</mi></math></span>-FWER for any <span><math><mi>k</mi></math></span> greater than one.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"241 ","pages":"Article 106311"},"PeriodicalIF":0.8,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655502","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}
Pub Date : 2025-07-09DOI: 10.1016/j.jspi.2025.106312
Shaohua Xu, Yongdao Zhou
Partially linear models are widely used in many scientific and engineering fields due to their flexibility and interpretability. However, the design of experiments for these models remains underexplored. This paper tackles the challenge of robust experimental design for partially linear models within a minimax framework, focusing on the simultaneous robustness of both the regression function and the basis function. We derive explicit forms of minimax designs for various scenarios, including partially linear models with and without interactions. These designs are shown to have analytical expressions, specifically as the product measure of the orthogonal array and the uniform measure. For practical implementation, we present the exact -point minimax design based on the qualitative–quantitative discrepancy. Simulation results indicate that the proposed minimax designs are robust and efficient, even when the assumed model faces moderate or large contamination, or when the model is misspecified. Finally, the practical applicability of our minimax designs is demonstrated through a synthetic data based on the Quinidine Kinetics dataset.
{"title":"Minimax designs for partially linear models","authors":"Shaohua Xu, Yongdao Zhou","doi":"10.1016/j.jspi.2025.106312","DOIUrl":"10.1016/j.jspi.2025.106312","url":null,"abstract":"<div><div>Partially linear models are widely used in many scientific and engineering fields due to their flexibility and interpretability. However, the design of experiments for these models remains underexplored. This paper tackles the challenge of robust experimental design for partially linear models within a minimax framework, focusing on the simultaneous robustness of both the regression function and the basis function. We derive explicit forms of minimax designs for various scenarios, including partially linear models with and without interactions. These designs are shown to have analytical expressions, specifically as the product measure of the orthogonal array and the uniform measure. For practical implementation, we present the exact <span><math><mi>n</mi></math></span>-point minimax design based on the qualitative–quantitative discrepancy. Simulation results indicate that the proposed minimax designs are robust and efficient, even when the assumed model faces moderate or large contamination, or when the model is misspecified. Finally, the practical applicability of our minimax designs is demonstrated through a synthetic data based on the Quinidine Kinetics dataset.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"241 ","pages":"Article 106312"},"PeriodicalIF":0.8,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144595498","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}
Pub Date : 2025-07-07DOI: 10.1016/j.jspi.2025.106316
Shengli Zhao, Tao Sun
Most existing criteria for selecting optimal fractional factorial designs consider the overall confounding of all effects and are proposed according to the effect hierarchy principle. However, in practical applications, especially when experimenters are interested in certain effects, the confounding information of individual effects is particularly important. We propose an individual aliased effect number pattern (I-AENP) for two-level designs to handle this situation and establish the relationship between I-AENP and the core patterns of several existing criteria. Some applications of the new pattern are discussed.
{"title":"Individual aliased effect number pattern for two-level designs and its applications","authors":"Shengli Zhao, Tao Sun","doi":"10.1016/j.jspi.2025.106316","DOIUrl":"10.1016/j.jspi.2025.106316","url":null,"abstract":"<div><div>Most existing criteria for selecting optimal fractional factorial designs consider the overall confounding of all effects and are proposed according to the effect hierarchy principle. However, in practical applications, especially when experimenters are interested in certain effects, the confounding information of individual effects is particularly important. We propose an individual aliased effect number pattern (I-AENP) for two-level designs to handle this situation and establish the relationship between I-AENP and the core patterns of several existing criteria. Some applications of the new pattern are discussed.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"241 ","pages":"Article 106316"},"PeriodicalIF":0.8,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144595497","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}
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