With the rapid development of modern computing techniques, high-dimensional data are increasingly encountered in many studies. In this paper, we propose a three-step method to study the mean testing problem. The proposed test is based on the p-values calculated from the univariate tests and the dimension reduction method. Since it does not require explicit conditions of data dimension and sample size, we can use it to solve the mean testing problem of high-dimensional data, especially when the data dimension is much larger than the sample size. The new method can be implemented for the normal and non-normal distribution, which has a wide application. Various simulations are conducted to compare the testing power of the new method and the existing tests. The comparison shows that the new method has higher testing power. We also apply the proposed method to a real example of gene expression data.
{"title":"A p-value based dimensionality reduction test for high dimensional means","authors":"Hongyan Fang, Chunyu Yao, Wenzhi Yang, Xuejun Wang, Huang Xu","doi":"10.1080/02331888.2023.2179627","DOIUrl":"https://doi.org/10.1080/02331888.2023.2179627","url":null,"abstract":"With the rapid development of modern computing techniques, high-dimensional data are increasingly encountered in many studies. In this paper, we propose a three-step method to study the mean testing problem. The proposed test is based on the p-values calculated from the univariate tests and the dimension reduction method. Since it does not require explicit conditions of data dimension and sample size, we can use it to solve the mean testing problem of high-dimensional data, especially when the data dimension is much larger than the sample size. The new method can be implemented for the normal and non-normal distribution, which has a wide application. Various simulations are conducted to compare the testing power of the new method and the existing tests. The comparison shows that the new method has higher testing power. We also apply the proposed method to a real example of gene expression data.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"58 1","pages":"282 - 299"},"PeriodicalIF":1.9,"publicationDate":"2023-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90038146","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 : 2023-02-23DOI: 10.1080/02331888.2023.2180003
Ping Zhao
This paper considers the problem of testing the presence of alpha in high-dimensional conditional time-varying factor model. We proposed a spatial-sign-based test procedure which is robust and efficient for heavy-tailed distributions. We established the theoretical properties of the proposed test statistic under some mild conditions. Simulation studies and a real data example also show the superior of our test procedure to the existing methods.
{"title":"Robust high-dimensional alpha test for conditional time-varying factor models","authors":"Ping Zhao","doi":"10.1080/02331888.2023.2180003","DOIUrl":"https://doi.org/10.1080/02331888.2023.2180003","url":null,"abstract":"This paper considers the problem of testing the presence of alpha in high-dimensional conditional time-varying factor model. We proposed a spatial-sign-based test procedure which is robust and efficient for heavy-tailed distributions. We established the theoretical properties of the proposed test statistic under some mild conditions. Simulation studies and a real data example also show the superior of our test procedure to the existing methods.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"255 1","pages":"444 - 457"},"PeriodicalIF":1.9,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77162772","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 : 2023-02-19DOI: 10.1080/02331888.2023.2179054
O. Arslan, Ş. Özdemir
Maximum likelihood estimation is a popular method for parameter estimation in regression models. However, since in some data sets it may not be possible to make any distributional assumptions on the error term, the likelihood method cannot be used to estimate the parameters of interest. For those data sets, one can use the empirical likelihood estimation method to estimate the parameters of a linear regression model. The aim of this study is to propose a robust penalized empirical likelihood estimation method to estimate the regression parameters and select significant variables, simultaneously, for data scenarios for which a well-defined likelihood function may not be available. This will be achieved by combining a robust empirical estimation method and the bridge penalty function. We investigate the asymptotic properties of the proposed estimator and explore the finite sample behaviour with a simulation study and a real data example.
{"title":"Robust penalized empirical likelihood estimation method for linear regression","authors":"O. Arslan, Ş. Özdemir","doi":"10.1080/02331888.2023.2179054","DOIUrl":"https://doi.org/10.1080/02331888.2023.2179054","url":null,"abstract":"Maximum likelihood estimation is a popular method for parameter estimation in regression models. However, since in some data sets it may not be possible to make any distributional assumptions on the error term, the likelihood method cannot be used to estimate the parameters of interest. For those data sets, one can use the empirical likelihood estimation method to estimate the parameters of a linear regression model. The aim of this study is to propose a robust penalized empirical likelihood estimation method to estimate the regression parameters and select significant variables, simultaneously, for data scenarios for which a well-defined likelihood function may not be available. This will be achieved by combining a robust empirical estimation method and the bridge penalty function. We investigate the asymptotic properties of the proposed estimator and explore the finite sample behaviour with a simulation study and a real data example.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"53 1","pages":"423 - 443"},"PeriodicalIF":1.9,"publicationDate":"2023-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91217352","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 : 2023-02-07DOI: 10.1080/02331888.2023.2174117
C. Nunes, Dário Ferreira, Sandra S. Ferreira, M. Fonseca, Manuela Oliveira, J. Mexia
Wishart matrices play an important role in normal multivariate statistical analysis. In this work, we present an approach that has been already used for normal vectors and is now applied to noncentral Wishart matrices. We show that, under general conditions, the vec of the Wishart matrix and a large class of its statistics have asymptotic normal distributions when the norm of the noncentrality parameter diverges ∞. These statistics are called smooth and are given by functions whose component functions have continuous second-order partial derivatives in a neighbourhood of a ‘pivot’ point. Moreover, we derive the application domain of the asymptotic normal distributions for the vec of the Wishart matrix and its smooth statistics. Thus we have an attraction to the normal model, for the increasing predominance of noncentrality and not for increasing sample sizes. A simulation study shows that the threshold for the use of asymptotic normal distributions is quite acceptable.
{"title":"Noncentral Wishart matrices, asymptotic normality of vec and smooth statistics","authors":"C. Nunes, Dário Ferreira, Sandra S. Ferreira, M. Fonseca, Manuela Oliveira, J. Mexia","doi":"10.1080/02331888.2023.2174117","DOIUrl":"https://doi.org/10.1080/02331888.2023.2174117","url":null,"abstract":"Wishart matrices play an important role in normal multivariate statistical analysis. In this work, we present an approach that has been already used for normal vectors and is now applied to noncentral Wishart matrices. We show that, under general conditions, the vec of the Wishart matrix and a large class of its statistics have asymptotic normal distributions when the norm of the noncentrality parameter diverges ∞. These statistics are called smooth and are given by functions whose component functions have continuous second-order partial derivatives in a neighbourhood of a ‘pivot’ point. Moreover, we derive the application domain of the asymptotic normal distributions for the vec of the Wishart matrix and its smooth statistics. Thus we have an attraction to the normal model, for the increasing predominance of noncentrality and not for increasing sample sizes. A simulation study shows that the threshold for the use of asymptotic normal distributions is quite acceptable.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"27 1","pages":"261 - 281"},"PeriodicalIF":1.9,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75344047","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 : 2023-01-02DOI: 10.1080/02331888.2023.2169689
Na Zou, H. Qin, K. Chatterjee
In this paper, we proposed the average Lee discrepancy to measure the uniformity of designs and studied its connection with the standard optimality measures used in the context of design of experiments. Lower bounds to such measure are provided as a benchmark to obtain uniform designs. We also defined the minimum average Lee-moment aberration criterion used to compare and screen the optimal design, and some lower bounds to such criterion are also provided.
{"title":"A study on average Lee discrepancy measure","authors":"Na Zou, H. Qin, K. Chatterjee","doi":"10.1080/02331888.2023.2169689","DOIUrl":"https://doi.org/10.1080/02331888.2023.2169689","url":null,"abstract":"In this paper, we proposed the average Lee discrepancy to measure the uniformity of designs and studied its connection with the standard optimality measures used in the context of design of experiments. Lower bounds to such measure are provided as a benchmark to obtain uniform designs. We also defined the minimum average Lee-moment aberration criterion used to compare and screen the optimal design, and some lower bounds to such criterion are also provided.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"62 1","pages":"53 - 70"},"PeriodicalIF":1.9,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78536434","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 : 2023-01-02DOI: 10.1080/02331888.2023.2172172
Sotirios Losidis
This paper initially presents bounds for the joint tail and the conditional tails of the backward and forward recurrence times. Using these bounds, we deliver an improvement to the lower bound for the renewal function given by Brown [Inequalities for distributions with increasing failure rate. In: Gelfand AE, editors. Contributions to the theory and applications of statistics, a volume in honour of Herbert Solomon. Orlando, FL: Academic; 1987. p. 3–17] for IFR inter-arrival times. Finally, this paper proposes a renewal type equation for the expected number of renewals in and, under certain conditions, improves Lorden's [On excess over the boundary. Ann Math Stat. 1970;41(2):520–527] well-known general upper bound for the expected number of renewals in .
{"title":"Recurrence times and the expected number of renewal epochs over a finite interval","authors":"Sotirios Losidis","doi":"10.1080/02331888.2023.2172172","DOIUrl":"https://doi.org/10.1080/02331888.2023.2172172","url":null,"abstract":"This paper initially presents bounds for the joint tail and the conditional tails of the backward and forward recurrence times. Using these bounds, we deliver an improvement to the lower bound for the renewal function given by Brown [Inequalities for distributions with increasing failure rate. In: Gelfand AE, editors. Contributions to the theory and applications of statistics, a volume in honour of Herbert Solomon. Orlando, FL: Academic; 1987. p. 3–17] for IFR inter-arrival times. Finally, this paper proposes a renewal type equation for the expected number of renewals in and, under certain conditions, improves Lorden's [On excess over the boundary. Ann Math Stat. 1970;41(2):520–527] well-known general upper bound for the expected number of renewals in .","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"100 1","pages":"195 - 212"},"PeriodicalIF":1.9,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81754637","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 : 2023-01-02DOI: 10.1080/02331888.2022.2161547
Cui-Juan Kong, Han-Ying Liang, Guoliang Fan
We, in this paper, focus on the inference of conditional quantile difference (CQD) for left-truncated and right-censored model. Based on local conditional likelihood function of the observed data, local likelihood ratio function and smoothed local log-likelihood ratio (log-SLL) of the CQD are constructed, and the maximum local likelihood estimator of the CQD is further defined from the log-SLL. When the observations are assumed to be a sequence of stationary α-mixing random variables, we establish asymptotic normality of the defined estimator, and prove the Wilks' theorem of adjusted log-SLL. Besides, we define another estimator of the CQD based on product-limit estimator of conditional distribution function and give its asymptotic normality. Also, simulation study and real data analysis are conducted to investigate the finite sample behaviour of the proposed methods.
{"title":"Local likelihood of quantile difference under left-truncated, right-censored and dependent assumptions","authors":"Cui-Juan Kong, Han-Ying Liang, Guoliang Fan","doi":"10.1080/02331888.2022.2161547","DOIUrl":"https://doi.org/10.1080/02331888.2022.2161547","url":null,"abstract":"We, in this paper, focus on the inference of conditional quantile difference (CQD) for left-truncated and right-censored model. Based on local conditional likelihood function of the observed data, local likelihood ratio function and smoothed local log-likelihood ratio (log-SLL) of the CQD are constructed, and the maximum local likelihood estimator of the CQD is further defined from the log-SLL. When the observations are assumed to be a sequence of stationary α-mixing random variables, we establish asymptotic normality of the defined estimator, and prove the Wilks' theorem of adjusted log-SLL. Besides, we define another estimator of the CQD based on product-limit estimator of conditional distribution function and give its asymptotic normality. Also, simulation study and real data analysis are conducted to investigate the finite sample behaviour of the proposed methods.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"37 1","pages":"71 - 93"},"PeriodicalIF":1.9,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79377587","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 : 2023-01-02DOI: 10.1080/02331888.2023.2168666
Siddhartha Chakraborty, Ritwik Bhattacharya, B. Pradhan
In this paper, joint cumulative entropy of progressive type-II censored order statistics is obtained in terms of reversed hazard rate function. Also, entropy and Kullback–Leibler information for progressive type-II censored order statistics are expressed using reversed hazard rate. Optimal life-testing plans based on cumulative entropy are proposed. Finally, cumulative entropy-based optimal designs using compound optimal design strategy for the life-testing experiment under progressive type-II censoring are developed. A real data set is analysed for illustration.
{"title":"Cumulative entropy of progressively type-II censored order statistics and associated optimal life testing-plans","authors":"Siddhartha Chakraborty, Ritwik Bhattacharya, B. Pradhan","doi":"10.1080/02331888.2023.2168666","DOIUrl":"https://doi.org/10.1080/02331888.2023.2168666","url":null,"abstract":"In this paper, joint cumulative entropy of progressive type-II censored order statistics is obtained in terms of reversed hazard rate function. Also, entropy and Kullback–Leibler information for progressive type-II censored order statistics are expressed using reversed hazard rate. Optimal life-testing plans based on cumulative entropy are proposed. Finally, cumulative entropy-based optimal designs using compound optimal design strategy for the life-testing experiment under progressive type-II censoring are developed. A real data set is analysed for illustration.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"39 1","pages":"161 - 174"},"PeriodicalIF":1.9,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89744970","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 : 2023-01-02DOI: 10.1080/02331888.2023.2172173
Jakob Peterlin, J. Stare, R. Blagus
Model checking plays an important role in parametric regression as model misspecification seriously affects the validity and efficiency of regression analysis. Model checks can be performed by constructing an empirical process from the model's fitted values and residuals. Due to a complex covariance function of the process obtaining the exact distribution of the test statistic is, however, intractable. Several solutions to overcome this have been proposed. It was shown that the simulation and bootstrap-based approaches are asymptotically valid, however, we show by using simulations that the rate of convergence can be slow. We, therefore, propose to estimate the null distribution by using a novel permutation-based procedure. We prove, under some mild assumptions, that this yields consistent tests under the null and some alternative hypotheses. Small sample properties of the proposed approach are studied in an extensive Monte Carlo simulation study and real data illustration is also provided.
{"title":"A permutation approach to goodness-of-fit testing in regression models","authors":"Jakob Peterlin, J. Stare, R. Blagus","doi":"10.1080/02331888.2023.2172173","DOIUrl":"https://doi.org/10.1080/02331888.2023.2172173","url":null,"abstract":"Model checking plays an important role in parametric regression as model misspecification seriously affects the validity and efficiency of regression analysis. Model checks can be performed by constructing an empirical process from the model's fitted values and residuals. Due to a complex covariance function of the process obtaining the exact distribution of the test statistic is, however, intractable. Several solutions to overcome this have been proposed. It was shown that the simulation and bootstrap-based approaches are asymptotically valid, however, we show by using simulations that the rate of convergence can be slow. We, therefore, propose to estimate the null distribution by using a novel permutation-based procedure. We prove, under some mild assumptions, that this yields consistent tests under the null and some alternative hypotheses. Small sample properties of the proposed approach are studied in an extensive Monte Carlo simulation study and real data illustration is also provided.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"18 1","pages":"123 - 149"},"PeriodicalIF":1.9,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72815174","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 : 2023-01-02DOI: 10.1080/02331888.2023.2168004
Victor Mooto Nawa, S. Nadarajah
Motivated by Zhao, Jang and Kim [Journal of Multivariate Analysis, 191, 2022, article number 105109], we propose new closed form estimators for a bivariate gamma distribution. The new estimators are simpler. In addition, they can have smaller asymptotic variances and smaller asymptotic covariances compared to Zhao et al.'s estimators and method of moments estimators. The new estimators can also perform better in real-data applications.
受Zhao, Jang和Kim [Journal of Multivariate Analysis, 1982,2022, article number 105109]的启发，我们提出了一种新的二元gamma分布的封闭形式估计。新的估算器更简单。此外，与Zhao等人的估计量和矩量估计量方法相比，它们可以具有较小的渐近方差和渐近协方差。新的估计器在实际数据应用中也有更好的表现。
{"title":"New closed form estimators for a bivariate gamma distribution","authors":"Victor Mooto Nawa, S. Nadarajah","doi":"10.1080/02331888.2023.2168004","DOIUrl":"https://doi.org/10.1080/02331888.2023.2168004","url":null,"abstract":"Motivated by Zhao, Jang and Kim [Journal of Multivariate Analysis, 191, 2022, article number 105109], we propose new closed form estimators for a bivariate gamma distribution. The new estimators are simpler. In addition, they can have smaller asymptotic variances and smaller asymptotic covariances compared to Zhao et al.'s estimators and method of moments estimators. The new estimators can also perform better in real-data applications.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"5 1","pages":"150 - 160"},"PeriodicalIF":1.9,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80093869","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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