抗击时流，守护经学——陈鼎忠的经学研究与《六艺后论》的经学思想

陈鼎忠是现代湖湘著名学者。他在疑古惑经思潮激荡的民国年间,坚持经学研究,甚至抗击时流,在《六艺后论》中批评疑古、惑经、非圣的思想主张,竭力维持经学的独立与尊严。尤其是在经学难以作为一门独立学科继续存在于现代文教体制的时代,他图谋构建"经之囊括万有"的学术文化新格局,想为经学在现代学术文化体系中谋取一席之位,乃至恢复经学统御众学的昔日荣光。陈鼎忠等现代学人在艰难时代守护经学的贡献,值得后人珍视。     

略论刘禹锡谪居朗州以后的文学创作思想

贬谪朗州对刘禹锡的诗文创作产生了重要影响 ,刘禹锡的“气干文支”、“立言寓言”和“辄立评议”的创作思想同韩愈的古文理论是互相呼应的 ,“氓谣俚音 ,可俪风什”更使其在学习民歌的基础上取得了极有价值的成就。     

正态回归模型中未知参数几种估计的比较分析

给出了正态回归模型中未知参数的无偏估计,最小二乘估计与极大似然估计及其求解过程,并通过数值模拟说明了异同点,验证了相应的结论。     

Quantile estimation for a progressively censored exponential distribution

Abstract

In this paper, we consider the problem of estimating the quantile of a two-parameter exponential distribution with respect to an arbitrary strictly convex loss function under progressive type II censoring. Inadmissibility of the best affine equivariant (BAE) estimator is established through a conditional risk analysis. In particular we provide dominance results for quadratic, linex and absolute value loss functions. Further, a class of dominating estimators is derived using the IERD (integral expression of risk difference) approach of Kubokawa (1994 Kubokawa, T. 1994. A unified approach to improving equivariant estimators. The Annals of Statistics 22 (1):290–9. doi:10.1214/aos/1176325369.[Crossref], [Web of Science ®] , [Google Scholar]). In sequel the generalized Bayes estimator is shown to improve the BAE estimator.     

An improved and efficient biased estimation technique in logistic regression model

Abstract

In this article, we propose a new improved and efficient biased estimation method which is a modified restricted Liu-type estimator satisfying some sub-space linear restrictions in the binary logistic regression model. We study the properties of the new estimator under the mean squared error matrix criterion and our results show that under certain conditions the new estimator is superior to some other estimators. Moreover, a Monte Carlo simulation study is conducted to show the performance of the new estimator in the simulated mean squared error and predictive median squared errors sense. Finally, a real application is considered.     

Nonparametric inference on mean residual life function with length-biased right-censored data

Abstract

In survival or reliability studies, the mean residual life (MRL) function is an important characteristic in understanding the survival or ageing process. In this article, we consider the problem of nonparametric MRL function estimation with length-biased right-censored data. Two nonparametric estimators of the MRL are proposed and their weak convergence is presented. In order to evaluate the performance of these estimators, small Monte Carlo simulations are carried out. Results show that the proposed estimators work well especially when the sample size is small and their calculations are simple. Finally, a real data example is provided.     

Nonparametric kernel estimation of expected shortfall under negatively associated sequences

Abstract

In this article, Bahadur type expansions of a nonparametric kernel estimator for ES under NA sequences are given. The strong consistency and the uniformly asymptotic normality of the estimator are yielded from the Bahadur type expansions, while the convergence rates of the above asymptotic properties are also obtained. Moreover, the expectation, the variance and the mean squared error (MSE) of the estimator are given. Besides, the optimal bandwidth selection of this estimator is discussed. We point out that all above results are based on the NA sequences. Finally, we conduct numerical simulations and compare performances of some ES estimators.     

Reliability analysis for stress-strength model from a general family of truncated distributions under censored data

Abstract

Under progressive Type-II censoring, inference of stress-strength reliability (SSR) is studied for a general family of lower truncated distributions. When the lifetime models of the strength and stress variables have arbitrary and common parameters, maximum likelihood and pivotal quantities based generalized estimators of SSR are established, respectively. Confidence intervals are constructed based on generalized pivotal quantities and bootstrap technique under different parameter cases as well. In addition, to compare the equivalence of the strength and stress parameters, likelihood ratio testing of interested parameters is provided as a complementary. Simulation studies and two real-life data examples are provided to investigate the performance of proposed methods.