{"title":"The proximal bootstrap for constrained estimators","authors":"Jessie Li","doi":"10.1016/j.jspi.2024.106245","DOIUrl":"10.1016/j.jspi.2024.106245","url":null,"abstract":"<div><div>We demonstrate how to conduct uniformly asymptotically valid inference for <span><math><msqrt><mrow><mi>n</mi></mrow></msqrt></math></span>-consistent estimators defined as the solution to a constrained optimization problem with a possibly nonsmooth or nonconvex sample objective function and a possibly nonconvex constraint set. We allow for the solution to the problem to be on the boundary of the constraint set or to drift towards the boundary of the constraint set as the sample size goes to infinity. We construct a confidence set by benchmarking a test statistic against critical values that can be obtained from a simple unconstrained quadratic programming problem. Monte Carlo simulations illustrate the uniformly correct coverage of our method in a boundary constrained maximum likelihood model, a boundary constrained nonsmooth GMM model, and a conditional logit model with capacity constraints.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142571397","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":"Testing the equality of distributions using integrated maximum mean discrepancy","authors":"Tianxuan Ding , Zhimei Li , Yaowu Zhang","doi":"10.1016/j.jspi.2024.106246","DOIUrl":"10.1016/j.jspi.2024.106246","url":null,"abstract":"<div><div>Comparing and testing for the homogeneity of two independent random samples is a fundamental statistical problem with many applications across various fields. However, existing methods may not be effective when the data is complex or high-dimensional. We propose a new method that integrates the maximum mean discrepancy (MMD) with a Gaussian kernel over all one-dimensional projections of the data. We derive the closed-form expression of the integrated MMD and prove its validity as a distributional similarity metric. We estimate the integrated MMD with the <span><math><mi>U</mi></math></span>-statistic theory and study its asymptotic behaviors under the null and two kinds of alternative hypotheses. We demonstrate that our method has the benefits of the MMD, and outperforms existing methods on both synthetic and real datasets, especially when the data is complex and high-dimensional.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553626","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":"Semiparametric estimation of a principal functional coefficient panel data model with cross-sectional dependence and its application to cigarette demand","authors":"Yan-Yong Zhao , Ling-Ling Ge , Kong-Sheng Zhang","doi":"10.1016/j.jspi.2024.106244","DOIUrl":"10.1016/j.jspi.2024.106244","url":null,"abstract":"<div><div>In this paper, we consider the estimation of functional coefficient panel data models with cross-sectional dependence. Borrowing the principal component structure, the functional coefficient panel data models can be transformed into a semiparametric panel data model. Combining the local linear dummy variable technique and profile least squares method, we develop a semiparametric profile method to estimate the coefficient functions. A gradient-descent iterative algorithm is employed to enhance computation speed and estimation accuracy. The main results show that the resulting parameter estimator enjoys asymptotic normality with a <span><math><msqrt><mrow><mi>N</mi><mi>T</mi></mrow></msqrt></math></span> convergence rate and the nonparametric estimator is asymptotically normal with a nonparametric convergence rate <span><math><msqrt><mrow><mi>N</mi><mi>T</mi><mi>h</mi></mrow></msqrt></math></span> when both the number of cross-sectional units <span><math><mi>N</mi></math></span> and the length of time series <span><math><mi>T</mi></math></span> go to infinity, under some regularity conditions. Monte Carlo simulations are carried out to evaluate the proposed methods, and an application to cigarette demand is investigated for illustration.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142416590","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":"A family of discrete maximum-entropy distributions","authors":"David J. Hessen","doi":"10.1016/j.jspi.2024.106243","DOIUrl":"10.1016/j.jspi.2024.106243","url":null,"abstract":"<div><div>In this paper, a family of maximum-entropy distributions with general discrete support is derived. Members of the family are distinguished by the number of specified non-central moments. In addition, a subfamily of discrete symmetric distributions is defined. Attention is paid to maximum likelihood estimation of the parameters of any member of the general family. It is shown that the parameters of any special case with infinite support can be estimated using a conditional distribution given a finite subset of the total support. In an empirical data example, the procedures proposed are demonstrated.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142416588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Risk minimization using robust experimental or sampling designs and mixture of designs","authors":"Ejub Talovic, Yves Tillé","doi":"10.1016/j.jspi.2024.106241","DOIUrl":"10.1016/j.jspi.2024.106241","url":null,"abstract":"<div><div>For both experimental and sampling designs, the efficiency or balance of designs has been extensively studied. There are many ways to incorporate auxiliary information into designs. However, when we use balanced designs to decrease the variance due to an auxiliary variable, the variance may increase due to an effect which we define as lack of robustness. This robustness can be written as the largest eigenvalue of the variance operator of a sampling or experimental design. If this eigenvalue is large, then it might induce a large variance in the Horvitz–Thompson estimator of the total. We calculate or estimate the largest eigenvalue of the most common designs. We determine lower, upper bounds and approximations of this eigenvalue for different designs. Then, we compare these results with simulations that show the trade-off between efficiency and robustness. Those results can be used to determine the proper choice of designs for experiments such as clinical trials or surveys. We also propose a new and simple method for mixing two sampling designs, which allows to use a tuning parameter between two sampling designs. This method is then compared to the Gram–Schmidt walk design, which also governs the trade-off between robustness and efficiency. A set of simulation studies shows that our method of mixture gives similar results to the Gram–Schmidt walk design while having an interpretable variance matrix.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142416589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal s-level fractional factorial designs under baseline parameterization","authors":"Zhaohui Yan, Shengli Zhao","doi":"10.1016/j.jspi.2024.106242","DOIUrl":"10.1016/j.jspi.2024.106242","url":null,"abstract":"<div><div>In this paper, we explore the minimum aberration criterion for <span><math><mi>s</mi></math></span>-level designs under baseline parameterization, called BP-MA. We give a complete search method and an incomplete search method to obtain the BP-MA (or nearly BP-MA) designs. The methodology has no restriction on <span><math><mi>s</mi></math></span>, the levels of the factors. The catalogues of (nearly) BP-MA designs with <span><math><mrow><mi>s</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn></mrow></math></span> levels are provided.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357419","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":"Shifted BH methods for controlling false discovery rate in multiple testing of the means of correlated normals against two-sided alternatives","authors":"Sanat K. Sarkar, Shiyu Zhang","doi":"10.1016/j.jspi.2024.106238","DOIUrl":"10.1016/j.jspi.2024.106238","url":null,"abstract":"<div><div>For simultaneous testing of multivariate normal means with known correlation matrix against two-sided alternatives, this paper introduces new methods with proven finite-sample control of false discovery rate. The methods are obtained by shifting each <span><math><mi>p</mi></math></span>-value to the left and considering a Benjamini–Hochberg-type linear step-up procedure based on these shifted <span><math><mi>p</mi></math></span>-values. The amount of shift for each <span><math><mi>p</mi></math></span>-value is appropriately determined from the correlation matrix to achieve the desired false discovery rate control. Simulation studies and real-data application show favorable performances of the proposed methods when compared with relevant competitors.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323239","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":"On schematic orthogonal arrays of high strength","authors":"Rong Yan, Shanqi Pang, Jing Wang, Mengqian Chen","doi":"10.1016/j.jspi.2024.106230","DOIUrl":"10.1016/j.jspi.2024.106230","url":null,"abstract":"<div><p>Schematic orthogonal arrays are closely related to association schemes. And which orthogonal arrays are schematic orthogonal arrays and how to classify them is an open problem proposed by Hedayat et al. (1999). By using the Hamming distances, this paper presents some general methods for constructing schematic symmetric and mixed orthogonal arrays of high strength. As applications of these methods, we construct association schemes and many new schematic orthogonal arrays including several infinite classes of such arrays. Some examples are provided to illustrate the construction methods. The paper gives the partial solution of the problem by Hedayat et al. (1999) for symmetric and mixed orthogonal arrays of high strength.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142162837","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}
Becky Tang , Henry A. Frye , John A. Silander Jr. , Alan E. Gelfand
{"title":"Zero-inflated multivariate tobit regression modeling","authors":"Becky Tang , Henry A. Frye , John A. Silander Jr. , Alan E. Gelfand","doi":"10.1016/j.jspi.2024.106229","DOIUrl":"10.1016/j.jspi.2024.106229","url":null,"abstract":"<div><p>A frequent challenge encountered in real-world applications is data having a high proportion of zeros. Focusing on ecological abundance data, much attention has been given to zero-inflated count data. Models for non-negative continuous abundance data with an excess of zeros are rarely discussed. Work presented here considers the creation of a point mass at zero through a left-censoring approach or through a hurdle approach. We incorporate both mechanisms to capture the analog of zero-inflation for count data. Additionally, primary attention has been given to univariate zero-inflated modeling (e.g., single species), whereas data often arise jointly (e.g., a collection of species). With multivariate abundance data, a key issue is to capture dependence among the species at a site, both in terms of positive abundance as well as absence. Therefore, our contribution is a model for multivariate zero-inflated continuous data that are non-negative. Working in a Bayesian framework, we discuss the issue of separating the two sources of zeros and offer model comparison metrics for multivariate zero-inflated data. In an application, we model the total biomass for five tree species obtained from plots established in the Forest Inventory Analysis database in the Northeast region of the United States.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142150410","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":"Convergent stochastic algorithm for estimation in general multivariate correlated frailty models using integrated partial likelihood","authors":"Ajmal Oodally , Luc Duchateau , Estelle Kuhn","doi":"10.1016/j.jspi.2024.106231","DOIUrl":"10.1016/j.jspi.2024.106231","url":null,"abstract":"<div><p>The Cox model with unspecified baseline hazard is often used to model survival data. In the case of correlated event times, this model can be extended by introducing random effects, also called frailty terms, leading to the frailty model. Few methods have been put forward to estimate parameters of such frailty models, and they often consider only a particular distribution for the frailty terms and specific correlation structures. In this paper, a new efficient method is introduced to perform parameter estimation by maximizing the integrated partial likelihood. The proposed stochastic estimation procedure can deal with frailty models with a broad choice of distributions for the frailty terms and with any kind of correlation structure between the frailty components, also allowing random interaction terms between the covariates and the frailty components. The almost sure convergence of the stochastic estimation algorithm towards a critical point of the integrated partial likelihood is proved. Numerical convergence properties are evaluated through simulation studies and comparison with existing methods is performed. In particular, the robustness of the proposed method with respect to different parametric baseline hazards and misspecified frailty distributions is demonstrated through simulation. Finally, the method is applied to a mastitis and a bladder cancer dataset.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142162836","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}