Statistical inference based on generalized Lindley record values

This paper addresses the problems of frequentist and Bayesian estimation for the unknown parameters of generalized Lindley distribution based on lower record values. We first derive the exact explicit expressions for the single and product moments of lower record values, and then use these results to compute the means, variances and covariance between two lower record values. We next obtain the maximum likelihood estimators and associated asymptotic confidence intervals. Furthermore, we obtain Bayes estimators under the assumption of gamma priors on both the shape and the scale parameters of the generalized Lindley distribution, and associated the highest posterior density interval estimates. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential (LINEX)) loss functions. Finally, we compute Bayesian predictive estimates and predictive interval estimates for the future record values. To illustrate the findings, one real data set is analyzed, and Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation and prediction.     

学术道路自述

回顾几十年来学术研究的道路,开始把鲁迅研究以专著形式系列化。这里的系列,只能说是“小系”,而不是“大系”。在这基础上,扩大研究领域,撰写关于中国现代小说研究,现代文学史研究的论著,同时进行散文创作,出版几本散文集。学术界的前辈、同辈、后辈的学者,在著作和文章中对我的论著、作品,进行热情的评论、分析,至感。     

夏文化探索中的方法问题——"夏商周断代工程"结题后的反思(二)

目前,学术界公认中国历史上有个夏代。但由于文献记载太过简略,使后人对当时的社会历史状况知之甚少。在这种情况下,人们寄希望于考古工作者从地下找到夏代遗存。然而,在夏文化探索中,由于研究者的思路与所用方法不同,故而得出的结论也明显有异。由此,出现争论与分歧。于是,如何鉴别相关结论是否合理可信就成为学术界同人思索的问题。本文在对夏文化探索的现状进行回顾的基础上,围绕文化因素分析法与都城分析法,对分歧及其缘由作了详细探讨。文中还就坚持正确思路,采用科学方法。按科学规程操作对夏文化探索工作的重要性,谈了自己的看法。     

教育贷款审计的方法研究

高校扩招的压力迫使高等学校通过贷款来筹集资金进行基础设施建设,随之因贷款资金而产生的腐败、犯罪行为也在不断增加。论文通过分析贷款资金的来源和使用情况,揭示了教育贷款容易滋生腐败的薄弱环节,提出了建立教育贷款专项审计制度和内部控制审计为主的教育贷款审计的新审计思路和新方法。     

浅议法律解释中的利益衡量法

文章从法律解释与利益衡量的关系出发,阐明利益衡量在民事审判中是有其存在的必要的。并在此基础上,探讨了法官在进行利益衡量时应使用哪些方法,排除哪些有碍利益衡量的因素,以及进行利益衡量时应考虑的利益原则和所负担的相当注意义务。     

On hysteretic vector autoregressive model with applications

This paper proposes a new hysteretic vector autoregressive (HVAR) model in which the regime switching may be delayed when the hysteresis variable lies in a hysteresis zone. We integrate an adapted multivariate Student-t distribution from amending the scale mixtures of normal distributions. This HVAR model allows for a higher degree of flexibility in the degrees of freedom for each time series. We use the proposed model to test for a causal relationship between any two target time series. Using posterior odds ratios, we overcome the limitations of the classical approach to multiple testing. Both simulated and real examples herein help illustrate the suggested methods. We apply the proposed HVAR model to investigate the causal relationship between the quarterly growth rates of gross domestic product of United Kingdom and United States. Moreover, we check the pairwise lagged dependence of daily PM2.5 levels in three districts of Taipei.     

Smoothed bootstrap bandwidth selection for nonparametric hazard rate estimation

A smoothed bootstrap method is presented for the purpose of bandwidth selection in nonparametric hazard rate estimation for iid data. In this context, two new bootstrap bandwidth selectors are established based on the exact expression of the bootstrap version of the mean integrated squared error of some approximations of the kernel hazard rate estimator. This is very useful since Monte Carlo approximation is no longer needed for the implementation of the two bootstrap selectors. A simulation study is carried out in order to show the empirical performance of the new bootstrap bandwidths and to compare them with other existing selectors. The methods are illustrated by applying them to a diabetes data set.     

Robust inference for estimating equations with nonignorably missing data based on SIR algorithm

Nonresponse is a very common phenomenon in survey sampling. Nonignorable nonresponse – that is, a response mechanism that depends on the values of the variable having nonresponse – is the most difficult type of nonresponse to handle. This article develops a robust estimation approach to estimating equations (EEs) by incorporating the modelling of nonignorably missing data, the generalized method of moments (GMM) method and the imputation of EEs via the observed data rather than the imputed missing values when some responses are subject to nonignorably missingness. Based on a particular semiparametric logistic model for nonignorable missing response, this paper proposes the modified EEs to calculate the conditional expectation under nonignorably missing data. We can apply the GMM to infer the parameters. The advantage of our method is that it replaces the non-parametric kernel-smoothing with a parametric sampling importance resampling (SIR) procedure to avoid nonparametric kernel-smoothing problems with high dimensional covariates. The proposed method is shown to be more robust than some current approaches by the simulations.     

Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

Empirical Bayes is a versatile approach to “learn from a lot” in two ways: first, from a large number of variables and, second, from a potentially large amount of prior information, for example, stored in public repositories. We review applications of a variety of empirical Bayes methods to several well‐known model‐based prediction methods, including penalized regression, linear discriminant analysis, and Bayesian models with sparse or dense priors. We discuss “formal” empirical Bayes methods that maximize the marginal likelihood but also more informal approaches based on other data summaries. We contrast empirical Bayes to cross‐validation and full Bayes and discuss hybrid approaches. To study the relation between the quality of an empirical Bayes estimator and p, the number of variables, we consider a simple empirical Bayes estimator in a linear model setting. We argue that empirical Bayes is particularly useful when the prior contains multiple parameters, which model a priori information on variables termed “co‐data”. In particular, we present two novel examples that allow for co‐data: first, a Bayesian spike‐and‐slab setting that facilitates inclusion of multiple co‐data sources and types and, second, a hybrid empirical Bayes–full Bayes ridge regression approach for estimation of the posterior predictive interval.     

Conditional design of the EWMA median chart with estimated parameters

The exponentially weighted moving average (EWMA) chart is often designed assuming the process parameters are known. In practice, the parameters are rarely known and need to be estimated from Phase I samples. Different Phase I samples are used when practitioners construct their own control chart's limits, which leads to the “Phase I between-practitioners” variability in the in-control average run length (ARL) of control charts. The standard deviation of the ARL (SDARL) is a good alternative to quantify this variability in control charts. Based on the SDARL metric, the performance of the EWMA median chart with estimated parameters is investigated in this paper. Some recommendations are given based on the SDARL metric. The results show that the EWMA median chart requires a much larger amount of Phase I data in order to reduce the variation in the in-control ARL up to a reasonable level. Due to the limitation of the amount of the Phase I data, the suggested EWMA median chart is designed with the bootstrap method which provides a good balance between the in-control and out-of-control ARL values.