Statistical Theory and Related Fields最新文献

{"title":"Bayesian quantile semiparametric mixed-effects double regression models","authors":"Duo Zhang, Liucang Wu, K. Ye, Min Wang","doi":"10.1080/24754269.2021.1877961","DOIUrl":"https://doi.org/10.1080/24754269.2021.1877961","url":null,"abstract":"Semiparametric mixed-effects double regression models have been used for analysis of longitudinal data in a variety of applications, as they allow researchers to jointly model the mean and variance of the mixed-effects as a function of predictors. However, these models are commonly estimated based on the normality assumption for the errors and the results may thus be sensitive to outliers and/or heavy-tailed data. Quantile regression is an ideal alternative to deal with these problems, as it is insensitive to heteroscedasticity and outliers and can make statistical analysis more robust. In this paper, we consider Bayesian quantile regression analysis for semiparametric mixed-effects double regression models based on the asymmetric Laplace distribution for the errors. We construct a Bayesian hierarchical model and then develop an efficient Markov chain Monte Carlo sampling algorithm to generate posterior samples from the full posterior distributions to conduct the posterior inference. The performance of the proposed procedure is evaluated through simulation studies and a real data application.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"303 - 315"},"PeriodicalIF":0.5,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1877961","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42904985","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":"Selecting baseline designs using a minimum aberration criterion when some two-factor interactions are important","authors":"Anqi Chen, Cheng-Yu Sun, Boxin Tang","doi":"10.1080/24754269.2020.1867795","DOIUrl":"https://doi.org/10.1080/24754269.2020.1867795","url":null,"abstract":"ABSTRACT This article considers the problem of selecting two-level designs under the baseline parameterisation when some two-factor interactions are important. We propose a minimum aberration criterion, which minimises the bias caused by the non-negligible effects. Using this criterion, a class of optimal designs can be further distinguished from one another, and we present an algorithm to find the minimum aberration designs among the D-optimal designs. Sixteen-run and twenty-run designs are summarised for practical use.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"95 - 101"},"PeriodicalIF":0.5,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2020.1867795","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47930848","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 system for determining maximum tolerated dose in clinical trial","authors":"K. Ye, Xiaobin Yang, Y. Ji, Min Wang","doi":"10.1080/24754269.2021.1871708","DOIUrl":"https://doi.org/10.1080/24754269.2021.1871708","url":null,"abstract":"Toxicity study, especially in determining the maximum tolerated dose (MTD) in phase I clinical trial, is an important step in developing new life-saving drugs. In practice, toxicity levels may be categorised as binary grades, multiple grades, or in a more generalised case, continuous grades. In this study, we propose an overall MTD framework that includes all the aforementioned cases for a single toxicity outcome (response). The mechanism of determining MTD involves a function that is predetermined by user. Analytic properties of such a system are investigated and simulation studies are performed for various scenarios. The concept of the continual reassessment method (CRM) is also implied in the framework and Bayesian analysis, including Markov chain Monte Carlo (MCMC) methods are used in estimating the model parameters.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"288 - 302"},"PeriodicalIF":0.5,"publicationDate":"2021-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1871708","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45763211","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":"Inference after covariate-adaptive randomisation: aspects of methodology and theory","authors":"J. Shao","doi":"10.1080/24754269.2021.1871873","DOIUrl":"https://doi.org/10.1080/24754269.2021.1871873","url":null,"abstract":"Covariate-adaptive randomisation has a more than 45 years of history of applications in clinical trials, in order to balance treatment assignments across prognostic factors that may have influence on the outcomes of interest. However, almost no theory had been developed for covariate-adaptive randomisation until a paper on the theory of testing hypotheses published in 2010. In this article, we review aspects of methodology and theory developed in the last decade for statistical inference under covariate-adaptive randomisation. We focus on issues such as whether a conventional procedure valid under the assumption that treatments are assigned completely at random is still valid or conservative when the actual randomisation is covariate-adaptive, how a valid inference procedure can be obtained by modifying a conventional method or directly constructed by stratifying the covariates used in randomisation, whether inference procedures have different properties when covariate-adaptive randomisation schemes have different degrees of balancing assignments, and how to further adjust covariates in the inference procedures to gain more efficiency. Recommendations are made during the review and further research problems are discussed.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"172 - 186"},"PeriodicalIF":0.5,"publicationDate":"2021-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1871873","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41476425","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":"Application of autoregressive tail-index model to China's stock market","authors":"Jingyu Ji, Deyuan Li","doi":"10.1080/24754269.2020.1862586","DOIUrl":"https://doi.org/10.1080/24754269.2020.1862586","url":null,"abstract":"We congratulate Professor Zhengjun Zhang for a topnotch contribution to the literature and thank the editor for the invitation to participate in the discussion of the excellent review paper. Zhang (2020) provides an informative summary ofmodelling systematic risk with nonlinear time series models and tail dependence measures based on extreme observations. In the current era, where risk management is becoming more and more important, this review paper is timely and will provide the impetus for future research in this and broader areas. Section 5.1 in Zhang (2020) proposes the autoregressive tail-index model to characterise and describe systematic risk and risk contagions. The autoregressive tail-index model is not only a good measure of systematic risk in the US stock market (Zhao et al., 2018), but can also be applied to the study of extreme climate (Deng et al., 2020) and other fields. In this discussion, we are more interested in whether the autoregressive tail-index model is also suitable to characterise the systematic risk in China’s stock market. We present an analysis of the stock negative log-returns of the Shanghai Composite Index (SSE Index), which is one of the most important indexes for China’s stock market. The data contains the daily closing prices of 180 components of SSE Index and is downloaded from WindFinancial Terminal from 01/05/2005 to 10/20/2020 with 3836 observations for each stock. Figure 1 plots the daily closing prices of SSE Index. Since SSE Index adjusts its component stocks every half year, we analyse 87 stocks that have always been included in the index from 01/05/2005 to 10/20/2020. For day t, we obtain 87 negative log-returns and calculate the maximaQ t = max1≤i≤87 ri,t , where ri,t is the daily negative log-return for stock i. Figure 2 shows the histogram of {Q t : t = 1, 2, . . . , 3836}. By Figure 2, we see that there are many daily maxima of negative log-returns clustered around 0.11, due to the Limit Up-Limit Down Rule of China’s stock market. This rule prohibits trading activity in exchangelisted securities at prices outside specified price bands. Motivated by Section 5.1 in Zhang (2020), we first fit a GARCH(1,1) model with normal distributed innovations to each individual negative log-retuens series. Using the negative log-returns series divided by the fitted volatilities, we obtain standardised negative log-returns series for each stock. Taking the maximum value of the 87 standardised negative log-returns each day, we obtain a time series {Qt : t = 1, 2, . . . , 3836}, see Figure 3. It is seen that there exist four possible peaks around June 2006, November 2008, January 2016 and September 2018. In fact, China’s stockmarket experienced substantial boom and burst during these five periods. On June 7, 2006, SSE Index plummeted 88.45 points. In 2008, the US subprime mortgage crisis spread to the world and triggered a financial tsunami. SSE Index dropped from the highest of 6124 in October 2007 to the lowest of ","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"31 - 34"},"PeriodicalIF":0.5,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2020.1862586","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47057017","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 of ‘On studying extreme values and systematic risks with nonlinear time series models and tail dependence measures’","authors":"Ting Zhang","doi":"10.1080/24754269.2020.1862587","DOIUrl":"https://doi.org/10.1080/24754269.2020.1862587","url":null,"abstract":"I congratulate and thank the author for providing a systematic and thorough review of both classical approaches and modern developments on the modelling of extremal events and tail dependence in th...","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"35 - 36"},"PeriodicalIF":0.5,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2020.1862587","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43054810","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":"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":"Discussion of ‘On studying extreme values and systematic risks with nonlinear time series models and tail dependence measures’","authors":"Tiandong Wang, Jun Yan","doi":"10.1080/24754269.2020.1869897","DOIUrl":"https://doi.org/10.1080/24754269.2020.1869897","url":null,"abstract":"We congratulate Prof. Zhang for this timely review on recent advances in extreme value theory for heterogeneous populations and on time series models for extreme observations. This is a substantial effort. Not only does it give a summary of the state-of-the-art work in time series modelling of extremes but also suggests interesting methodological and applied research questions. Our discussion focuses on extremal dependence metrics and practical applications for the time series models.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"38 - 40"},"PeriodicalIF":0.5,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2020.1869897","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46431347","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}