Statistical Theory and Related Fields最新文献

{"title":"Rejoinder of “On studying extreme values and systematic risks with nonlinear time series models and tail dependence measures”","authors":"Zhengjun Zhang","doi":"10.1080/24754269.2021.1871710","DOIUrl":"https://doi.org/10.1080/24754269.2021.1871710","url":null,"abstract":"I am pleased that my review article has stimulated such broader and thoughtful discussions in probability theory, theoretical statistics, estimation methods, and applications. The discussants have made many excellent points. I appreciate the discussants’ interest in the reviewed contents and much broader theoretical and methodological topics related to extreme value study. In particular, Ji and Li (2021), find a way that one of the reviewed models can be extended to study the systematic risks in the Chinese stock market. Qi (2021) points out that the estimation of the static tail index parameter in the generalised extreme value distribution is still far from perfect, and then discusses three maximum likelihood estimations from Hall (1982), Peng and Qi (2009), and F. Wang et al. (2019) to handle the tail index that falls in different ranges. Smith (2021) offers a much more general view of the development of extreme value theory over the last thirty years. Readers can benefit from reading the discussions and the references discussed therein. T. Wang and Yan (2021) not only extend discussions to two extreme dependence measures introduced by Resnick (2004) and Davis and Mikosch (2009) but also point out some practical issues existed in many extreme value applications. Xu andWang (2021) show some interesting ideas of extending the tail quotient correlation coefficient to the conditional tail quotient correlation coefficient for conditional tail independence. They also outline some ideas of applying the new extreme value theory formaxima of maxima for high-dimensional inference, e.g., multiple testing problems. T. Zhang (2021a) focuses on time series extremes and advocates measuring the cumulative tail adversarial effect, i.e., the degree of serial tail dependence and the desired limit theorem in T. Zhang (2021b). My review is focussing on studying extreme values and systematic risks with nonlinear time series models and tail dependence measures, and of course, it is not the final word on the reviewed topics and the topics discussed by the discussants, and many other broad topics researched by the extreme value literature. I look forward to future developments in all of these areas. This rejoinder will further clarify some basic ideas behind each reviewed measures, models, their applications, and their further developments. Interpretability, computability, and testability. Some basic properties, such as interpretability, computability, predictability, stability, and testability, are often desired in statistical applications. In general, parametric models can satisfy these properties and are widely adopted. For example, linear regressions are the most popular models used daily, and Pearson’s linear correlation coefficient is the most commonly used dependence measure between two random variables. On the other hand, parametric models may not be general enough, and their models’ assumptions may not be satisfied. As a result, nonparametric (semi-parametric)","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"45 - 48"},"PeriodicalIF":0.5,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1871710","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44507983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discussion on paper ‘On studying extreme values and systematic risks with nonlinear time series models and tail dependence measures’ by Zhengjun Zhang","authors":"Y. Qi","doi":"10.1080/24754269.2020.1862589","DOIUrl":"https://doi.org/10.1080/24754269.2020.1862589","url":null,"abstract":"I would like to take this opportunity to congratulate Zhengjun for his continuing contribution to extremevalue statistics in recent years. In this review paper, some fundamental theories on univariate extremes and multivariate extremes are introduced, and recent developments on extremes from some structured stochastic processes are also given. The results in the latter sections of the paper are largely due to Zhengjun and his coauthors. The paper provides some insights for future challenges on extremes and can help young researchers follow the contemporary research topics. Below I offer some comments onunivariate extremevalue statistics. Although the theory for univariate extremes is quite complete, the statistical methods such as the estimation and inference procedures are far from perfect. Set μ = 0 and σ = 1 in the definition (2.6) in the paper and write","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"37 - 37"},"PeriodicalIF":0.5,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2020.1862589","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44024206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multivariate extremes and max-stable processes: discussion of the paper by Zhengjun Zhang","authors":"R. Smith","doi":"10.1080/24754269.2021.1871709","DOIUrl":"https://doi.org/10.1080/24754269.2021.1871709","url":null,"abstract":"This discussion reviews the paper by Zhengjun Zhang in the context of broader research on multivariate extreme value theory and max-stable processes.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"41 - 44"},"PeriodicalIF":0.5,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1871709","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48749651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discussion on “on studying extreme values and systematic risks with nonlinear time series models and tail dependence measures”","authors":"Wen Xu, Huixia Judy Wang","doi":"10.1080/24754269.2021.1895528","DOIUrl":"https://doi.org/10.1080/24754269.2021.1895528","url":null,"abstract":"Extreme value theory provides essential mathematical foundations for modelling tail risks and has wide applications. The emerging of big and heterogeneous data calls for the development of new extreme value theory and methods. For studying high-dimensional extremes and extreme clusters in time series, an important problem is how to measure and test for tail dependence between random variables. Section 3.1 of Dr. Zhang’s paper discusses some newly proposed tail dependence measures. In the era of big data, a timely and challenging question is how to study data from heterogeneous populations, e.g. from different sources. Section 3.2 reviews some new developments of extreme value theory for maxima of maxima. The theory and methods in Sections 3.1 and 2.3 set the foundations for modelling extremes of multivariate and heterogeneous data, and we believe they have wide applicability. We will discuss two possible directions: (1) measuring and testing of partial tail dependence; (2) application of the extreme value theory for maxima of maxima in highdimensional inference.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"26 - 30"},"PeriodicalIF":0.5,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1895528","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43522771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Covariance estimation via fiducial inference.","authors":"W Jenny Shi,&nbsp;Jan Hannig,&nbsp;Randy C S Lai,&nbsp;Thomas C M Lee","doi":"10.1080/24754269.2021.1877950","DOIUrl":"https://doi.org/10.1080/24754269.2021.1877950","url":null,"abstract":"<p><p>As a classical problem, covariance estimation has drawn much attention from the statistical community for decades. Much work has been done under the frequentist and the Bayesian frameworks. Aiming to quantify the uncertainty of the estimators without having to choose a prior, we have developed a fiducial approach to the estimation of covariance matrix. Built upon the Fiducial Berstein-von Mises Theorem (Sonderegger and Hannig 2014), we show that the fiducial distribution of the covariate matrix is consistent under our framework. Consequently, the samples generated from this fiducial distribution are good estimators to the true covariance matrix, which enable us to define a meaningful confidence region for the covariance matrix. Lastly, we also show that the fiducial approach can be a powerful tool for identifying clique structures in covariance matrices.</p>","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 4","pages":"316-331"},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1877950","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33442561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear prediction via Hermite transformation","authors":"T. McElroy, Srinjoy Das","doi":"10.1080/24754269.2020.1856589","DOIUrl":"https://doi.org/10.1080/24754269.2020.1856589","url":null,"abstract":"ABSTRACT General prediction formulas involving Hermite polynomials are developed for time series expressed as a transformation of a Gaussian process. The prediction gains over linear predictors are examined numerically, demonstrating the improvement of nonlinear prediction.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"49 - 54"},"PeriodicalIF":0.5,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2020.1856589","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44941464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonignorable item nonresponse in panel data","authors":"Sijing Li, J. Shao","doi":"10.1080/24754269.2020.1856591","DOIUrl":"https://doi.org/10.1080/24754269.2020.1856591","url":null,"abstract":"To estimate unknown population parameters based on panel data having nonignorable item nonresponse, we propose an innovative data grouping approach according to the number of observed components in the multivariate outcome when the joint distribution of and associated covariate is nonparametric and the nonresponse probability conditional on and has a parametric form. To deal with the identifiability issue, we utilise a nonresponse instrument , an auxiliary variable related to but not related to the nonresponse probability conditional on and . We apply a modified generalised method of moments to obtain estimators of the parameters in the nonresponse probability, and a generalised regression estimation to utilise covariate information for efficient estimation of population parameters. Consistency and asymptotic normality of the proposed estimators of the population parameters are established. Simulation and real data results are presented.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"6 1","pages":"58 - 71"},"PeriodicalIF":0.5,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2020.1856591","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42460662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Research on three-step accelerated gradient algorithm in deep learning","authors":"Yongqiang Lian, Yincai Tang, Shirong Zhou","doi":"10.1080/24754269.2020.1846414","DOIUrl":"https://doi.org/10.1080/24754269.2020.1846414","url":null,"abstract":"Gradient descent (GD) algorithm is the widely used optimisation method in training machine learning and deep learning models. In this paper, based on GD, Polyak's momentum (PM), and Nesterov accelerated gradient (NAG), we give the convergence of the algorithms from an initial value to the optimal value of an objective function in simple quadratic form. Based on the convergence property of the quadratic function, two sister sequences of NAG's iteration and parallel tangent methods in neural networks, the three-step accelerated gradient (TAG) algorithm is proposed, which has three sequences other than two sister sequences. To illustrate the performance of this algorithm, we compare the proposed algorithm with the three other algorithms in quadratic function, high-dimensional quadratic functions, and nonquadratic function. Then we consider to combine the TAG algorithm to the backpropagation algorithm and the stochastic gradient descent algorithm in deep learning. For conveniently facilitate the proposed algorithms, we rewite the R package ‘neuralnet’ and extend it to ‘supneuralnet’. All kinds of deep learning algorithms in this paper are included in ‘supneuralnet’ package. Finally, we show our algorithms are superior to other algorithms in four case studies.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"6 1","pages":"40 - 57"},"PeriodicalIF":0.5,"publicationDate":"2020-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2020.1846414","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44709557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Covariate balancing based on kernel density estimates for controlled experiments","authors":"Yiou Li, Lulu Kang, Xiao Huang","doi":"10.1080/24754269.2021.1878742","DOIUrl":"https://doi.org/10.1080/24754269.2021.1878742","url":null,"abstract":"ABSTRACT Controlled experiments are widely used in many applications to investigate the causal relationship between input factors and experimental outcomes. A completely randomised design is usually used to randomly assign treatment levels to experimental units. When covariates of the experimental units are available, the experimental design should achieve covariate balancing among the treatment groups, such that the statistical inference of the treatment effects is not confounded with any possible effects of covariates. However, covariate imbalance often exists, because the experiment is carried out based on a single realisation of the complete randomisation. It is more likely to occur and worsen when the size of the experimental units is small or moderate. In this paper, we introduce a new covariate balancing criterion, which measures the differences between kernel density estimates of the covariates of treatment groups. To achieve covariate balance before the treatments are randomly assigned, we partition the experimental units by minimising the criterion, then randomly assign the treatment levels to the partitioned groups. Through numerical examples, we show that the proposed partition approach can improve the accuracy of the difference-in-mean estimator and outperforms the complete randomisation and rerandomisation approaches.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"102 - 113"},"PeriodicalIF":0.5,"publicationDate":"2020-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1878742","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41800210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A three-parameter logistic regression model","authors":"Xiaoli Yu, Shaoting Li, Jiahua Chen","doi":"10.1080/24754269.2020.1796098","DOIUrl":"https://doi.org/10.1080/24754269.2020.1796098","url":null,"abstract":"Dose–response experiments and data analyses are often carried out according to an optimal design under a model assumption. A two-parameter logistic model is often used because of its nice mathematical properties and plausible stochastic response mechanisms. There is an extensive literature on its optimal designs and data analysis strategies. However, a model is at best a good approximation in a real-world application, and researchers must be aware of the risk of model mis-specification. In this paper, we investigate the effectiveness of the sequential ED-design, the D-optimal design, and the up-and-down design under the three-parameter logistic regression model, and we develop a numerical method for the parameter estimation. Simulations show that the combination of the proposed model and the data analysis strategy performs well. When the logistic model is correct, this more complex model has hardly any efficiency loss. The three-parameter logistic model works better than the two-parameter logistic model in the presence of model mis-specification.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"265 - 274"},"PeriodicalIF":0.5,"publicationDate":"2020-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2020.1796098","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46183255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}