Pub Date : 2025-11-28DOI: 10.1016/j.jmva.2025.105551
Wenjuan Li , Hongming Pei , Ali Jiang , Fei Chen
In the sufficient dimension reduction (SDR), many methods depend on some assumptions on the distribution of predictor vector, such as the linear design condition (L.D.C.), the assumption of constant conditional variance, and so on. The mixture distributions emerge frequently in practice, but they may not satisfy the above assumptions. In this article, a general framework is proposed to extend various SDR methods to the cases where the predictor vector follows the mixture elliptical distributions, together with the asymptotic property for the consistency of the kernel matrix estimators. For illustration, the extensions of several classical SDR approaches under the proposed framework are detailed. Moreover, a method to estimate the structural dimension is given, together with a procedure to check an assumption called homogeneity. The proposed methodology is illustrated by simulated and real examples.
{"title":"A general framework to extend sufficient dimension reductions to the cases of the mixture multivariate elliptical distributions","authors":"Wenjuan Li , Hongming Pei , Ali Jiang , Fei Chen","doi":"10.1016/j.jmva.2025.105551","DOIUrl":"10.1016/j.jmva.2025.105551","url":null,"abstract":"<div><div>In the sufficient dimension reduction (SDR), many methods depend on some assumptions on the distribution of predictor vector, such as the linear design condition (L.D.C.), the assumption of constant conditional variance, and so on. The mixture distributions emerge frequently in practice, but they may not satisfy the above assumptions. In this article, a general framework is proposed to extend various SDR methods to the cases where the predictor vector follows the mixture elliptical distributions, together with the asymptotic property for the consistency of the kernel matrix estimators. For illustration, the extensions of several classical SDR approaches under the proposed framework are detailed. Moreover, a method to estimate the structural dimension is given, together with a procedure to check an assumption called homogeneity. The proposed methodology is illustrated by simulated and real examples.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"213 ","pages":"Article 105551"},"PeriodicalIF":1.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145683764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-28DOI: 10.1016/j.jmva.2025.105561
Shu-Yu Li , Han-Ying Liang , Bao-Hua Wang
We, in this paper, focus on partial linear varying-coefficient quantile regression with fixed effects under panel data and missing observations, where the missing observations include either responses or covariates are missing at random. Under independent setting, we define estimators of the unknown parameter vector, varying-coefficient function and effect in the model, and discuss their large number properties. To use the information from within-subject correlations, we propose weighted estimators for the unknown amounts, where the weights are chosen based on mean and quantile regressions, respectively, by quadratic inference technique and empirical likelihood method. Under dependent assumption, we establish asymptotic normality of the weighted estimators. Meanwhile, we study hypothesis tests of the parameter, varying-coefficient function and effect, and prove asymptotic distributions of restricted estimators and test statistics of the parameter under null hypothesis and local alternative hypothesis, respectively. Also, oracle property of the parameter is considered. Simulation study and real data analysis are conducted to evaluate the performance of the proposed methods.
{"title":"Varying-coefficient quantile regression with effect under panel data and missing observation","authors":"Shu-Yu Li , Han-Ying Liang , Bao-Hua Wang","doi":"10.1016/j.jmva.2025.105561","DOIUrl":"10.1016/j.jmva.2025.105561","url":null,"abstract":"<div><div>We, in this paper, focus on partial linear varying-coefficient quantile regression with fixed effects under panel data and missing observations, where the missing observations include either responses or covariates are missing at random. Under independent setting, we define estimators of the unknown parameter vector, varying-coefficient function and effect in the model, and discuss their large number properties. To use the information from within-subject correlations, we propose weighted estimators for the unknown amounts, where the weights are chosen based on mean and quantile regressions, respectively, by quadratic inference technique and empirical likelihood method. Under dependent assumption, we establish asymptotic normality of the weighted estimators. Meanwhile, we study hypothesis tests of the parameter, varying-coefficient function and effect, and prove asymptotic distributions of restricted estimators and test statistics of the parameter under null hypothesis and local alternative hypothesis, respectively. Also, oracle property of the parameter is considered. Simulation study and real data analysis are conducted to evaluate the performance of the proposed methods.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105561"},"PeriodicalIF":1.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145681897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-28DOI: 10.1016/j.jmva.2025.105574
Yuan Liu , Yan-Yong Zhao , Noriszura Ismail , Razik Ridzuan Mohd Tajuddin , Yuchun Zhang
Measurement error regression is widely used in statistical modeling. When the regression function is discontinuous, the estimation and inference have become challenging. In this paper, we develop a jump detection framework for a single index model with measurement error. First, for the single index model with measurement error, the consistent estimator of the index coefficient is obtained by using both the SIMEX (simulation extrapolation) and estimation equation methods. Then, the one-sided kernel local linear method is used to construct the estimator of the nonparametric function and the estimator of the jump point. Under some regularity assumptions, the asymptotic properties of the resultant estimators are established. The finite sample performance of our methodologies is evaluated by numerical simulation, and finally they are used to analyze the effect of serum cholesterol level and age on male blood.
{"title":"Jump detection in single-index models with measurement error","authors":"Yuan Liu , Yan-Yong Zhao , Noriszura Ismail , Razik Ridzuan Mohd Tajuddin , Yuchun Zhang","doi":"10.1016/j.jmva.2025.105574","DOIUrl":"10.1016/j.jmva.2025.105574","url":null,"abstract":"<div><div>Measurement error regression is widely used in statistical modeling. When the regression function is discontinuous, the estimation and inference have become challenging. In this paper, we develop a jump detection framework for a single index model with measurement error. First, for the single index model with measurement error, the consistent estimator of the index coefficient is obtained by using both the SIMEX (simulation extrapolation) and estimation equation methods. Then, the one-sided kernel local linear method is used to construct the estimator of the nonparametric function and the estimator of the jump point. Under some regularity assumptions, the asymptotic properties of the resultant estimators are established. The finite sample performance of our methodologies is evaluated by numerical simulation, and finally they are used to analyze the effect of serum cholesterol level and age on male blood.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105574"},"PeriodicalIF":1.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145616473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-28DOI: 10.1016/j.jmva.2025.105562
Jiajuan Liang , Peter M. Bentler , Yiwen Cao
Multivariate normality is a common assumption in the maximum likelihood analysis of two-level structural equation models. Under the normal assumption, the independence condition on level-1 observations is no longer satisfied. As a result, existing statistics for testing multivariate normality based independent observations cannot be directly used for the same purpose in two-level structural equation models. In this paper we tackle this problem by employing the theory of spherical matrix distributions and some properties of invariant statistics. A series of necessary tests are constructed from some existing invariant statistics with a balanced level-1 sample design. These necessary tests are applicable without requiring a large level-1 or level-2 sample size. A Monte Carlo study is carried out to demonstrate the performance of the proposed tests in the aspects of controlling type I error rates, the power against a departure from multivariate normality for level-1 variables, and the power against a departure from multivariate normality for level-2 variables. An application of the necessary tests to a practical data set is illustrated.
{"title":"Testing multivariate normality for two-level structural equation models","authors":"Jiajuan Liang , Peter M. Bentler , Yiwen Cao","doi":"10.1016/j.jmva.2025.105562","DOIUrl":"10.1016/j.jmva.2025.105562","url":null,"abstract":"<div><div>Multivariate normality is a common assumption in the maximum likelihood analysis of two-level structural equation models. Under the normal assumption, the independence condition on level-1 observations is no longer satisfied. As a result, existing statistics for testing multivariate normality based independent observations cannot be directly used for the same purpose in two-level structural equation models. In this paper we tackle this problem by employing the theory of spherical matrix distributions and some properties of invariant statistics. A series of necessary tests are constructed from some existing invariant statistics with a balanced level-1 sample design. These necessary tests are applicable without requiring a large level-1 or level-2 sample size. A Monte Carlo study is carried out to demonstrate the performance of the proposed tests in the aspects of controlling type I error rates, the power against a departure from multivariate normality for level-1 variables, and the power against a departure from multivariate normality for level-2 variables. An application of the necessary tests to a practical data set is illustrated.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105562"},"PeriodicalIF":1.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145616475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-28DOI: 10.1016/j.jmva.2025.105566
Xueyan Huang, Rui Qiu, Zhou Yu
In this paper, we introduce two Fréchet inverse regression methods with kernel bandwidths determined by nearest neighbors, designed to achieve sufficient dimension reduction for a metric space-valued response and Euclidean predictors. A key advantage of the proposals lies in their ability to effectively preserve the intrinsic information of the metric space-valued response. We establish the asymptotic normality of these methods through rigorous theoretical proofs. Additionally, simulations and a real data example are provided to validate the performance and practical applicability of the proposed methods.
{"title":"Fréchet kNN-based sufficient dimension reduction","authors":"Xueyan Huang, Rui Qiu, Zhou Yu","doi":"10.1016/j.jmva.2025.105566","DOIUrl":"10.1016/j.jmva.2025.105566","url":null,"abstract":"<div><div>In this paper, we introduce two Fréchet inverse regression methods with kernel bandwidths determined by <span><math><mi>k</mi></math></span> nearest neighbors, designed to achieve sufficient dimension reduction for a metric space-valued response and Euclidean predictors. A key advantage of the proposals lies in their ability to effectively preserve the intrinsic information of the metric space-valued response. We establish the asymptotic normality of these methods through rigorous theoretical proofs. Additionally, simulations and a real data example are provided to validate the performance and practical applicability of the proposed methods.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105566"},"PeriodicalIF":1.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145681887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-28DOI: 10.1016/j.jmva.2025.105556
Claire Geldenhuys, Rene Ehlers, Andriette Bekker
An extensive body of literature exists that specifically addresses the univariate case of zero-inflated count models. In contrast, research pertaining to multivariate models is notably less developed. We propose two new parsimonious multivariate models that can be used to model correlated multivariate overdispersed count data. Furthermore, for different parameter settings and sample sizes, various simulations are performed. In conclusion, we demonstrate the performance of the newly proposed multivariate candidates on two benchmark datasets, which surpasses that of several alternative approaches.
{"title":"Type I multivariate Pólya-Aeppli distributions with applications","authors":"Claire Geldenhuys, Rene Ehlers, Andriette Bekker","doi":"10.1016/j.jmva.2025.105556","DOIUrl":"10.1016/j.jmva.2025.105556","url":null,"abstract":"<div><div>An extensive body of literature exists that specifically addresses the univariate case of zero-inflated count models. In contrast, research pertaining to multivariate models is notably less developed. We propose two new parsimonious multivariate models that can be used to model correlated multivariate overdispersed count data. Furthermore, for different parameter settings and sample sizes, various simulations are performed. In conclusion, we demonstrate the performance of the newly proposed multivariate candidates on two benchmark datasets, which surpasses that of several alternative approaches.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105556"},"PeriodicalIF":1.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145681888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-28DOI: 10.1016/j.jmva.2025.105572
Yongshuai Chen , Gongming Shi , Xiaomeng Yan, Baoxue Zhang
In this paper, we study the limiting distribution of Chen-Qin’s test statistic and propose a novel weighted bootstrap test procedure for the high-dimensional two-sample Behrens–Fisher problem. We first show that the test statistic has an asymptotic null that is a mixture of a chi-square-type mixture distribution and a normal distribution, without imposing either the normal assumption or a factor-like model assumption on the underlying distributions. To gain insight into the asymptotic null distribution of the test statistic, we show that under stronger restrictions on the covariance matrices and the null hypothesis, the test statistic is either asymptotically normal or a chi-square-type mixture distribution. The power properties of the test are evaluated asymptotically under the high-dimensional local and fixed alternative hypothesis. We also derive that the proposed weighted bootstrap test procedure has correct test level asymptotically. Two simulation studies and a real data example show that the new weighted bootstrap procedure significantly outperforms other benchmarks in terms of size control and is comparable in terms of power.
{"title":"On the two-sample Behrens–Fisher problem for high-dimensional data","authors":"Yongshuai Chen , Gongming Shi , Xiaomeng Yan, Baoxue Zhang","doi":"10.1016/j.jmva.2025.105572","DOIUrl":"10.1016/j.jmva.2025.105572","url":null,"abstract":"<div><div>In this paper, we study the limiting distribution of Chen-Qin’s test statistic and propose a novel weighted bootstrap test procedure for the high-dimensional two-sample Behrens–Fisher problem. We first show that the test statistic has an asymptotic null that is a mixture of a chi-square-type mixture distribution and a normal distribution, without imposing either the normal assumption or a factor-like model assumption on the underlying distributions. To gain insight into the asymptotic null distribution of the test statistic, we show that under stronger restrictions on the covariance matrices and the null hypothesis, the test statistic is either asymptotically normal or a chi-square-type mixture distribution. The power properties of the test are evaluated asymptotically under the high-dimensional local and fixed alternative hypothesis. We also derive that the proposed weighted bootstrap test procedure has correct test level asymptotically. Two simulation studies and a real data example show that the new weighted bootstrap procedure significantly outperforms other benchmarks in terms of size control and is comparable in terms of power.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105572"},"PeriodicalIF":1.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145681890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-19DOI: 10.1016/j.jmva.2025.105548
Jing Yu , Jianxin Pan
A large number of explanatory variables may be measured with the collection of longitudinal data, of which some may not be influential for modeling of heterogeneous longitudinal data. For such complex data, not only their mean but also covariances may be affected by various explanatory variables. A data-driven approach is proposed to model the mean and covariance structures, simultaneously, together with selecting influential explanatory variables. A penalized maximum likelihood method for the joint mean and covariance model is developed within the framework of finite Gaussian mixture regression. EM algorithm is employed for the numerical calculation. The parameter estimators obtained are shown to be consistent and asymptotically normally distributed, and have oracle properties with proper choices of penalty function and tuning parameter. Simulation studies show that the proposed method works very well and provides accurate and effective parameter estimators by conducting variable selection. For illustration, real data analysis on clustering COVID-19 infected cases for European countries in terms of governmental policy effects is made to demonstrate the usefulness of the proposed method.
{"title":"Variable selection in mixture regression for longitudinal data based on joint mean–covariance model","authors":"Jing Yu , Jianxin Pan","doi":"10.1016/j.jmva.2025.105548","DOIUrl":"10.1016/j.jmva.2025.105548","url":null,"abstract":"<div><div>A large number of explanatory variables may be measured with the collection of longitudinal data, of which some may not be influential for modeling of heterogeneous longitudinal data. For such complex data, not only their mean but also covariances may be affected by various explanatory variables. A data-driven approach is proposed to model the mean and covariance structures, simultaneously, together with selecting influential explanatory variables. A penalized maximum likelihood method for the joint mean and covariance model is developed within the framework of finite Gaussian mixture regression. EM algorithm is employed for the numerical calculation. The parameter estimators obtained are shown to be consistent and asymptotically normally distributed, and have oracle properties with proper choices of penalty function and tuning parameter. Simulation studies show that the proposed method works very well and provides accurate and effective parameter estimators by conducting variable selection. For illustration, real data analysis on clustering COVID-19 infected cases for European countries in terms of governmental policy effects is made to demonstrate the usefulness of the proposed method.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105548"},"PeriodicalIF":1.4,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145571180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-19DOI: 10.1016/j.jmva.2025.105542
Fadoua Balabdaoui , Harald Besdziek , Yong Wang
The conditional independence assumption has recently appeared in a growing body of literature on the estimation of multivariate mixtures. We consider here conditionally independent multivariate mixtures of power series distributions with infinite support, to which belong Poisson, Geometric or Negative Binomial mixtures. We show that for all these mixtures, the non-parametric maximum likelihood estimator converges to the truth at the rate in the Hellinger distance, where denotes the size of the observed sample and represents the dimension of the mixture. Using this result, we then construct a new non-parametric estimator based on the maximum likelihood estimator that converges with the parametric rate in all -distances, for . These convergences rates are supported by simulations and the theory is illustrated using the famous Vélib dataset of the bike sharing system of Paris. We also introduce a testing procedure for whether the conditional independence assumption is satisfied for a given sample. This testing procedure is applied for several multivariate mixtures, with varying levels of dependence, and is thereby shown to distinguish well between conditionally independent and dependent mixtures. Finally, we use this testing procedure to investigate whether conditional independence holds for Vélib dataset.
{"title":"Parametric convergence rate of a non-parametric estimator in multivariate mixtures of power series distributions under conditional independence","authors":"Fadoua Balabdaoui , Harald Besdziek , Yong Wang","doi":"10.1016/j.jmva.2025.105542","DOIUrl":"10.1016/j.jmva.2025.105542","url":null,"abstract":"<div><div>The conditional independence assumption has recently appeared in a growing body of literature on the estimation of multivariate mixtures. We consider here conditionally independent multivariate mixtures of power series distributions with infinite support, to which belong Poisson, Geometric or Negative Binomial mixtures. We show that for all these mixtures, the non-parametric maximum likelihood estimator converges to the truth at the rate <span><math><mrow><msup><mrow><mrow><mo>(</mo><mo>ln</mo><mrow><mo>(</mo><mi>n</mi><mi>d</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>+</mo><mi>d</mi><mo>/</mo><mn>2</mn></mrow></msup><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span> in the Hellinger distance, where <span><math><mi>n</mi></math></span> denotes the size of the observed sample and <span><math><mi>d</mi></math></span> represents the dimension of the mixture. Using this result, we then construct a new non-parametric estimator based on the maximum likelihood estimator that converges with the parametric rate <span><math><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span> in all <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-distances, for <span><math><mrow><mi>p</mi><mo>≥</mo><mn>1</mn></mrow></math></span>. These convergences rates are supported by simulations and the theory is illustrated using the famous Vélib dataset of the bike sharing system of Paris. We also introduce a testing procedure for whether the conditional independence assumption is satisfied for a given sample. This testing procedure is applied for several multivariate mixtures, with varying levels of dependence, and is thereby shown to distinguish well between conditionally independent and dependent mixtures. Finally, we use this testing procedure to investigate whether conditional independence holds for Vélib dataset.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105542"},"PeriodicalIF":1.4,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145571181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates a constrained spatial autoregressive panel data model with fixed effects, partially linear time-varying coefficients, and time-varying spatial dependence. We propose a constrained profile two-stage least squares estimator and establish its asymptotic properties. Furthermore, a statistical test is constructed to examine whether the constant coefficients satisfy pre-specified linear constraints. Monte Carlo simulations under both independent and -mixing error structures demonstrate the finite-sample performance of the proposed estimators and testing procedure. A real data example is provided to illustrate the practical applicability of the method. In addition, when the time dimension is relatively small, a Block Bootstrap procedure is proposed to compute the -value for the test.
{"title":"Estimation for partially time-varying spatial autoregressive panel data model under linear constraints","authors":"Lingling Tian , Chuanhua Wei , Bing Sun , Mixia Wu","doi":"10.1016/j.jmva.2025.105547","DOIUrl":"10.1016/j.jmva.2025.105547","url":null,"abstract":"<div><div>This paper investigates a constrained spatial autoregressive panel data model with fixed effects, partially linear time-varying coefficients, and time-varying spatial dependence. We propose a constrained profile two-stage least squares estimator and establish its asymptotic properties. Furthermore, a statistical test is constructed to examine whether the constant coefficients satisfy pre-specified linear constraints. Monte Carlo simulations under both independent and <span><math><mi>α</mi></math></span>-mixing error structures demonstrate the finite-sample performance of the proposed estimators and testing procedure. A real data example is provided to illustrate the practical applicability of the method. In addition, when the time dimension <span><math><mi>T</mi></math></span> is relatively small, a Block Bootstrap procedure is proposed to compute the <span><math><mi>p</mi></math></span>-value for the test.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105547"},"PeriodicalIF":1.4,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145571182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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