长风呼啸 马蹄声碎——司马迁笔下的楚汉相争

秦朝灭亡后,刘邦与项羽两人争夺天下,司马迁称之为平乱诛暴的统一战争,史称楚汉相争。司马迁在《史记》中,通过汉中对策、下邑划策、成皋对峙、垓下决战的描述,反映了项羽凭的是力、善于征战,而刘邦凭的是智、用谋略取胜,最后刘邦集团谋略智计战胜了自矜武力的项羽集团。     

Stein-type estimation using ranked set sampling

In this study, we consider the application of the James–Stein estimator for population means from a class of arbitrary populations based on ranked set sample (RSS). We consider a basis for optimally combining sample information from several data sources. We succinctly develop the asymptotic theory of simultaneous estimation of several means for differing replications based on the well-defined shrinkage principle. We showcase that a shrinkage-type estimator will have, under quadratic loss, a substantial risk reduction relative to the classical estimator based on simple random sample and RSS. Asymptotic distributional quadratic biases and risks of the shrinkage estimators are derived and compared with those of the classical estimator. A simulation study is used to support the asymptotic result. An over-riding theme of this study is that the shrinkage estimation method provides a powerful extension of its traditional counterpart for non-normal populations. Finally, we will use a real data set to illustrate the computation of the proposed estimators.     

Generalized Method of Moments Estimation When a Parameter Is on a Boundary

This article establishes the asymptotic distributions of generalized method of moments (GMM) estimators when the true parameter lies on the boundary of the parameter space. The conditions allow the estimator objective function to be nonsmooth and to depend on preliminary estimators. The boundary of the parameter space may be curved and/or kinked. The article discusses three examples: (1) instrumental variables (IV) estimation of a regression model with nonlinear equality and/or inequality restrictions on the parameters; (2) method of simulated moments estimation of a multinomial discrete response model with some random coefficient variances equal to 0, some random effect variances equal to 0, or some measurement error variances equal to 0; and (3) semiparametric least squares estimation of a partially linear regression model with nonlinear equality and/or inequality restrictions on the parameters.     

On Small Sample Properties of the Wald,LR and LM Tests in a Linear Model with AR(1) Errors

When the error terms are autocorrelated, the conventional t-tests for individual regression coefficients mislead us to over-rejection of the null hypothesis. We examine, by Monte Carlo experiments, the small sample properties of the unrestricted estimator of ρ and of the estimator of ρ restricted by the null hypothesis. We compare the small sample properties of the Wald, likelihood ratio and Lagrange multiplier test statistics for individual regression coefficients. It is shown that when the null hypothesis is true, the unrestricted estimator of ρ is biased. It is also shown that the Lagrange multiplier test using the maximum likelihood estimator of ρ performs better than the Wald and likelihood ratio tests.     

Conditional Quantile Estimation for Truncated and Associated Data

Abstract

In survival or reliability studies, it is common to have data which are not only incomplete but weakly dependent too. Random truncation and censoring are two common forms of such data when they are neither independent nor strongly mixing but rather associated. The focus of this paper is on estimating conditional distribution and conditional quantile functions for randomly left truncated data satisfying association condition. We aim at deriving strong uniform consistency rates and asymptotic normality for the estimators and thereby, extend to association case some results stated under iid and α-mixing hypotheses. The performance of the quantile function estimator is evaluated on simulated data sets.     

Asymptotic design and estimation using linear splines

The estimation of a regression function g using linear splines is considered. The integrated mean square error is minimized using choice of estimator, allocation of observations and displacement of knots.     

刘锦棠与近代新疆的开发和建设

刘锦棠是新疆近代历史上的一位重要人物。他率军收复新疆失地 ;力主新疆建省 ,废除维吾尔族腐朽落后的伯克制 ;轻徭薄赋 ,移民实边 ;在新疆广设义塾 ,对少数民族实行汉化教育。他在军事、政治、经济、文化教育等方面 ,对近代新疆的开发和建设作出了巨大贡献     

Bayesian estimation of parameters of mixed geometric failure models from Type I group censored sample

The estimation problem of the parameters of a mixed geometric lifetime model, using Bayesian approach and Type I group censored sample, will be investigated in the case of two subpopulations. The Bayes estimates are derived for squared error, minimum expected, general entropy and linex loss functions under informative and diffuse priors. A practical example given by Nelson (W.B. Nelson, Hazard plotting methods for analysis of the life data with different failure models, J. Qual. Technol. 2 (1970), pp. 126–149) is considered. A simulation study is carried out along with risk.     

The existence of the mean of the estimator in seemingly unrelated regressions

The purpose of this note is to spell out the conditions for the existence of the mean of the coefficient; estimator in seemingly unrelated regressions.