Pub Date : 2023-07-01DOI: 10.1080/02331888.2023.2231114
Y. Linke, I. Borisov, P. Ruzankin
Consistent weighted least square estimators are proposed for a wide class of nonparametric regression models with random regression function, where this real-valued random function of k arguments is assumed to be continuous with probability 1. We obtain explicit upper bounds for the rate of uniform convergence in probability of the new estimators to the unobservable random regression function for both fixed or random designs. In contrast to the predecessors' results, the bounds for the convergence are insensitive to the correlation structure of the k-variate design points. As an application, we study the problem of estimating the mean and covariance functions of random fields with additive noise under dense data conditions. The theoretical results of the study are illustrated by simulation examples which show that the new estimators are more accurate in some cases than the Nadaraya–Watson ones. An example of processing real data on earthquakes in Japan in 2012–2021 is included.
{"title":"Universal kernel-type estimation of random fields","authors":"Y. Linke, I. Borisov, P. Ruzankin","doi":"10.1080/02331888.2023.2231114","DOIUrl":"https://doi.org/10.1080/02331888.2023.2231114","url":null,"abstract":"Consistent weighted least square estimators are proposed for a wide class of nonparametric regression models with random regression function, where this real-valued random function of k arguments is assumed to be continuous with probability 1. We obtain explicit upper bounds for the rate of uniform convergence in probability of the new estimators to the unobservable random regression function for both fixed or random designs. In contrast to the predecessors' results, the bounds for the convergence are insensitive to the correlation structure of the k-variate design points. As an application, we study the problem of estimating the mean and covariance functions of random fields with additive noise under dense data conditions. The theoretical results of the study are illustrated by simulation examples which show that the new estimators are more accurate in some cases than the Nadaraya–Watson ones. An example of processing real data on earthquakes in Japan in 2012–2021 is included.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"19 1","pages":"785 - 810"},"PeriodicalIF":1.9,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75038894","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 : 2023-06-27DOI: 10.1080/02331888.2023.2227984
S. Zheng, Fei Zhang, Chunhua Wang, Xuejun Wang
In this paper, we study the weak convergence and convergence rate in the weak law of large numbers for weighted sums of a class of random variables satisfying the Rosenthal type inequality. The necessary and sufficient conditions for the convergence rates in the weak law of large numbers under some mild conditions are provided. Moreover, the main results that we established are applied to simple linear errors-in-variables regression models and nonparametric regression models based on a class of random errors. Finally, we present some numerical simulations to assess the finite sample performance of the theoretical results.
{"title":"Weak convergence for weighted sums of a class of random variables with related statistical applications","authors":"S. Zheng, Fei Zhang, Chunhua Wang, Xuejun Wang","doi":"10.1080/02331888.2023.2227984","DOIUrl":"https://doi.org/10.1080/02331888.2023.2227984","url":null,"abstract":"In this paper, we study the weak convergence and convergence rate in the weak law of large numbers for weighted sums of a class of random variables satisfying the Rosenthal type inequality. The necessary and sufficient conditions for the convergence rates in the weak law of large numbers under some mild conditions are provided. Moreover, the main results that we established are applied to simple linear errors-in-variables regression models and nonparametric regression models based on a class of random errors. Finally, we present some numerical simulations to assess the finite sample performance of the theoretical results.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"8 1","pages":"867 - 899"},"PeriodicalIF":1.9,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80197517","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 : 2023-06-20DOI: 10.1080/02331888.2023.2225668
Chao Lu, Houlin Zhou, Xuejun Wang
In this paper, we establish the uniformly asymptotic normality for sample quantiles based on martingale difference sequences under some suitable conditions. We obtain the rate of normality approximation of by using some classical methods such as Bernstein type inequality, and so on. Finally, we verify asymptotic normality for the fixed quantile of the martingale difference sequences and present some numerical simulations to demonstrate the finite sample performances of the theoretical results.
{"title":"A Berry–Esseen theorem for sample quantiles under martingale difference sequences","authors":"Chao Lu, Houlin Zhou, Xuejun Wang","doi":"10.1080/02331888.2023.2225668","DOIUrl":"https://doi.org/10.1080/02331888.2023.2225668","url":null,"abstract":"In this paper, we establish the uniformly asymptotic normality for sample quantiles based on martingale difference sequences under some suitable conditions. We obtain the rate of normality approximation of by using some classical methods such as Bernstein type inequality, and so on. Finally, we verify asymptotic normality for the fixed quantile of the martingale difference sequences and present some numerical simulations to demonstrate the finite sample performances of the theoretical results.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"46 1","pages":"844 - 866"},"PeriodicalIF":1.9,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73445108","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 : 2023-06-05DOI: 10.1080/02331888.2023.2221363
E. Gonçalves, N. Mendes-Lopes
ABSTRACT An integer-valued ARCH process with a conditional zero-inflated binomial distribution is introduced. Stationarity, ergodicity and the autocovariance structure are studied as well as the estimation of parameters by conditional maximum likelihood. Numerical studies and an application to the number of hours in a day in which the prices of electricity for Portugal and Spain are different illustrate the performance of this model when compared with others.
{"title":"Zero-inflated binomial integer-valued ARCH models for time series","authors":"E. Gonçalves, N. Mendes-Lopes","doi":"10.1080/02331888.2023.2221363","DOIUrl":"https://doi.org/10.1080/02331888.2023.2221363","url":null,"abstract":"ABSTRACT An integer-valued ARCH process with a conditional zero-inflated binomial distribution is introduced. Stationarity, ergodicity and the autocovariance structure are studied as well as the estimation of parameters by conditional maximum likelihood. Numerical studies and an application to the number of hours in a day in which the prices of electricity for Portugal and Spain are different illustrate the performance of this model when compared with others.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"53 1","pages":"764 - 784"},"PeriodicalIF":1.9,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90098715","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 : 2023-05-04DOI: 10.1080/02331888.2023.2209817
Mojammel Haque Sarkar, M. Tripathy
The problem of estimating reciprocals of scale parameters (hazard rates) from two exponential populations with a common location and ordered scale parameters have been considered under the progressive type-II censoring scheme from a decision-theoretic viewpoint. The loss function is considered as quadratic. The maximum-likelihood estimators (MLEs) and the uniformly minimum variance unbiased estimators (UMVUEs) are derived. Sufficient conditions are derived for improving estimators in affine and scale equivariant classes. Consequently, improved estimators over the MLEs and the UMVUEs are derived. A numerical comparison among all the proposed estimators is made, and conclusions are drawn regarding their performances with respect to the quadratic loss function.
{"title":"Estimating reciprocals of scale parameters of two exponential populations with common location and ordered scales using censored samples","authors":"Mojammel Haque Sarkar, M. Tripathy","doi":"10.1080/02331888.2023.2209817","DOIUrl":"https://doi.org/10.1080/02331888.2023.2209817","url":null,"abstract":"The problem of estimating reciprocals of scale parameters (hazard rates) from two exponential populations with a common location and ordered scale parameters have been considered under the progressive type-II censoring scheme from a decision-theoretic viewpoint. The loss function is considered as quadratic. The maximum-likelihood estimators (MLEs) and the uniformly minimum variance unbiased estimators (UMVUEs) are derived. Sufficient conditions are derived for improving estimators in affine and scale equivariant classes. Consequently, improved estimators over the MLEs and the UMVUEs are derived. A numerical comparison among all the proposed estimators is made, and conclusions are drawn regarding their performances with respect to the quadratic loss function.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"2 1","pages":"710 - 739"},"PeriodicalIF":1.9,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73423719","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 : 2023-05-04DOI: 10.1080/02331888.2023.2213460
Yi Wu, T. Hu, Andrei Volodin, Xuejun Wang
In this paper, we mainly establish a general form of Berry–Esséen bound for α-mixing random variables. With different choices of the parameters, the rates are shown as , , and approximately . These results improved some corresponding ones in the literature. An application to the Berry–Esséen bound of sample quantiles is further provided. Moreover, some simulations are also carried out to support the theoretical results.
{"title":"Some improved results on Berry–Esséen bounds for strong mixing random variables and applications","authors":"Yi Wu, T. Hu, Andrei Volodin, Xuejun Wang","doi":"10.1080/02331888.2023.2213460","DOIUrl":"https://doi.org/10.1080/02331888.2023.2213460","url":null,"abstract":"In this paper, we mainly establish a general form of Berry–Esséen bound for α-mixing random variables. With different choices of the parameters, the rates are shown as , , and approximately . These results improved some corresponding ones in the literature. An application to the Berry–Esséen bound of sample quantiles is further provided. Moreover, some simulations are also carried out to support the theoretical results.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"263 1","pages":"740 - 760"},"PeriodicalIF":1.9,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79699989","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 : 2023-04-27DOI: 10.1080/02331888.2023.2204438
Yao Xiao, Shiqi Wang, H. Qin, J. Ning
Uniform designs seek to distribute design points uniformly in the experimental domain. Some discrepancies have been developed to measure the uniformity by treating all factors equally. It is reasonable when there exists no prior information about the system or when the potential model is completely unclear. However, in the situation of sequential designs, experimental information, such as the importance of each factor, would be obtained from previous stage experiments. With this fact, the weighted -discrepancy is more suitable than the original discrepancy for choosing follow-up designs. In this paper, the sequentially weighted uniform design is proposed, which is obtained by minimizing the weighted -discrepancy. The weights, indicating the relative importance of each factor, are estimated through a Bayesian hierarchical Gaussian process method based on serial experimental data. Results from several classic computer simulator examples, as well as a real application in circuit design, demonstrate that the performance of our new method surpasses that of its counterparts.
{"title":"Sequentially weighted uniform designs","authors":"Yao Xiao, Shiqi Wang, H. Qin, J. Ning","doi":"10.1080/02331888.2023.2204438","DOIUrl":"https://doi.org/10.1080/02331888.2023.2204438","url":null,"abstract":"Uniform designs seek to distribute design points uniformly in the experimental domain. Some discrepancies have been developed to measure the uniformity by treating all factors equally. It is reasonable when there exists no prior information about the system or when the potential model is completely unclear. However, in the situation of sequential designs, experimental information, such as the importance of each factor, would be obtained from previous stage experiments. With this fact, the weighted -discrepancy is more suitable than the original discrepancy for choosing follow-up designs. In this paper, the sequentially weighted uniform design is proposed, which is obtained by minimizing the weighted -discrepancy. The weights, indicating the relative importance of each factor, are estimated through a Bayesian hierarchical Gaussian process method based on serial experimental data. Results from several classic computer simulator examples, as well as a real application in circuit design, demonstrate that the performance of our new method surpasses that of its counterparts.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"25 1","pages":"534 - 553"},"PeriodicalIF":1.9,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81881742","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 : 2023-04-25DOI: 10.1080/02331888.2023.2206661
Kan Wang, Hong Qin, Zujun Ou
The purpose of this paper is to study the issue of employing the uniformity criterion measured by the mixture discrepancy to assess the optimal foldover plans for q-level factorials. The average mixture discrepancy and the average projection mixture discrepancy based on the level permutation method are respectively defined for combined designs, and the optimal foldover plan in terms of the overall uniformity and the uniformity of each dimension are also explored. The tight lower bounds of the average mixture discrepancy and the uniformity pattern under the general foldover plan are obtained respectively, which can be used as a benchmark for searching optimal foldover plans. Some illustrative examples are provided to show the theoretical results.
{"title":"Uniformity and projection uniformity of combined designs","authors":"Kan Wang, Hong Qin, Zujun Ou","doi":"10.1080/02331888.2023.2206661","DOIUrl":"https://doi.org/10.1080/02331888.2023.2206661","url":null,"abstract":"The purpose of this paper is to study the issue of employing the uniformity criterion measured by the mixture discrepancy to assess the optimal foldover plans for q-level factorials. The average mixture discrepancy and the average projection mixture discrepancy based on the level permutation method are respectively defined for combined designs, and the optimal foldover plan in terms of the overall uniformity and the uniformity of each dimension are also explored. The tight lower bounds of the average mixture discrepancy and the uniformity pattern under the general foldover plan are obtained respectively, which can be used as a benchmark for searching optimal foldover plans. Some illustrative examples are provided to show the theoretical results.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"17 1","pages":"515 - 533"},"PeriodicalIF":1.9,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82137948","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 : 2023-04-24DOI: 10.1080/02331888.2023.2203491
Niladri Chakraborty, N. Balakrishnan, M. Finkelstein
A new double sampling-based precedence and weighted precedence tests are introduced and analysed. The joint distributions of two precedence and weighted precedence statistics are obtained under the double-sampling framework. Subsequently, the closed-form expressions for the rejection probabilities are derived under the null hypothesis and the Lehmann alternative. The corresponding power comparison is carried out against the Lehmann alternative and the location-scale alternative through Monte-Carlo simulations. Finally, a couple of detailed illustrative examples are presented.
{"title":"On precedence tests with double sampling","authors":"Niladri Chakraborty, N. Balakrishnan, M. Finkelstein","doi":"10.1080/02331888.2023.2203491","DOIUrl":"https://doi.org/10.1080/02331888.2023.2203491","url":null,"abstract":"A new double sampling-based precedence and weighted precedence tests are introduced and analysed. The joint distributions of two precedence and weighted precedence statistics are obtained under the double-sampling framework. Subsequently, the closed-form expressions for the rejection probabilities are derived under the null hypothesis and the Lehmann alternative. The corresponding power comparison is carried out against the Lehmann alternative and the location-scale alternative through Monte-Carlo simulations. Finally, a couple of detailed illustrative examples are presented.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"48 1","pages":"554 - 576"},"PeriodicalIF":1.9,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80609717","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 : 2023-04-24DOI: 10.1080/02331888.2023.2203492
Tulika Rudra Gupta, Markus Pauly, Somesh Kumar
In design and development of products in various industries, a key characteristic is stress–strength reliability. In this article, we consider estimation of a new stress–strength index for several exponential populations with a common location. We derive various estimators such as the maximum likelihood, the uniformly minimum variance unbiased (UMVU), and Bayes estimators. We additionally apply Brewster–Zidek technique for improving upon estimators based on UMVU or best affine equivariant estimators of scale parameters. We derive the asymptotic distribution of the ML estimator and prove that the Bayes estimators' limit under a suitable prior distribution is a generalized Bayes estimator. We then evaluate the risk performance of the obtained estimators in an extensive simulation study. Two applications are given on real data sets to illustrate the new methods. One example relates to the duration analysis and the other to a problem of comparing strengths of different fibres in jute industry.
{"title":"Estimating a new stress–strength index for several exponential populations with a common location","authors":"Tulika Rudra Gupta, Markus Pauly, Somesh Kumar","doi":"10.1080/02331888.2023.2203492","DOIUrl":"https://doi.org/10.1080/02331888.2023.2203492","url":null,"abstract":"In design and development of products in various industries, a key characteristic is stress–strength reliability. In this article, we consider estimation of a new stress–strength index for several exponential populations with a common location. We derive various estimators such as the maximum likelihood, the uniformly minimum variance unbiased (UMVU), and Bayes estimators. We additionally apply Brewster–Zidek technique for improving upon estimators based on UMVU or best affine equivariant estimators of scale parameters. We derive the asymptotic distribution of the ML estimator and prove that the Bayes estimators' limit under a suitable prior distribution is a generalized Bayes estimator. We then evaluate the risk performance of the obtained estimators in an extensive simulation study. Two applications are given on real data sets to illustrate the new methods. One example relates to the duration analysis and the other to a problem of comparing strengths of different fibres in jute industry.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"32 1","pages":"669 - 693"},"PeriodicalIF":1.9,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84395484","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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