On generalized moment identity and its applications: a unified approach

In this paper, we obtain a generalized moment identity for the case when the distributions of the random variables are not necessarily purely discrete or absolutely continuous. The proposed identity is useful to find the generator which has been used for the approximation of distributions by Stein's method. Apparently, a new approach is discussed for the approximation of distributions by Stein's method. We bring the characterization based on the relationship between conditional expectations and hazard measure in our unified framework. As an application, a new lower bound to the mean-squared error is obtained and it is compared with Bayesian Cramer–Rao bound.     

On similarity and independence properties of composite edf goodness-of-fit tests

Many test statistics for classical simple goodness-of-fit hypothesis testing problems are distancemeasures between the distribution function of the null hypothesis distributipn and the empirical distribution function sometimes called EDF tests. If a composite parametric null hypothesis is considered in place of the simple null hypothesis, then a test statistic can be obtained from each EDF test by replacing the known distribution function of the simple problem by the Rao-Blackwell estimating distribution function. In this note we use known results to show that these Rao-Blackwell-EDF test statistics have distributions that do not depend upon parameter values, and hence that these tests are independent of a complete sufficient statistic for the parameters.     

饶应祺与新疆防务

饶应祺于1895年署理甘肃新疆巡抚。甘肃河湟事变发生后,严重威胁到新疆地区的稳定和安宁。饶应祺运筹帷幄,制定了防之境外的策略,事后又精心料理善后。他响应清廷振军经武的号召,在新疆实心举办团练、编练保甲、更新武器装备、采用新式操练方法等,对推动新疆地区的防务和军事近代化发挥了重要作用。义和团运动时期,又力主仿效东南互保,制定了合理可行的防守计划,保卫了新疆地区的安宁。     

Generalized Bhaskar Rao designs

Generalized Bhaskar Rao designs with non-zero elements from an abelian group G are constructed. In particular this paper shows that the necessary conditions are sufficient for the existence of generalized Bhaskar Rao designs with k=3 for the following groups: ?G? is odd, G=Z^r₂, and G=Z^r₂×H where 3? ?H? and r?1. It also constructs generalized Bhaskar Rao designs with υ=k, which is equivalent to υ rows of a generalized Hadamard matrix of order n where υ?n.     

建国初华东区保存富农政策执行情况解析

新中国成立初期，中共中央针对新区土地改革制定了保存富农经济的政策。在实际执行政策过程中，华东区根据地方调查情况，较好地执行了保存富农经济的政策。华东区之所以能较好的执行保存富农经济的政策，是与华东区农村调查的客观情况和地方领导人主观思想两个方面分不开的。这为建国初华东区经济的迅速恢复和发展创造了条件。     

饶宗颐与《潮州志》间的乡邦人文因素探究

饶宗颐先生总纂《潮州志》体现着与乡邦人文、潮州文化紧密相关的三个联系:修志的规模及条件与人文环境的联系;特殊历史时期与历史的制高点的联系;行政区划的变革与方志冠名的联系。饶宗颐先生总纂《潮州志》,客观上更是跟乡邦文化紧密相关甚至是乡邦人文因素起支配作用而推动的一种文化行为。     

Kshirsagar-Type Lower Bounds for Mean Squared Error of Prediction

Let Y be an observable random vector and Z be an unobserved random variable with joint density f(y, z | θ), where θ is an unknown parameter vector. Considering the problem of predicting Z based on Y, we derive Kshirsagar type lower bounds for the mean squared error of any predictor of Z. These bounds do not require the regularity conditions of Bhattacharyya bounds and hence are more widely applicable. Moreover, the new bounds are shown to be sharper than the corresponding Bhattacharyya bounds. The conditions for attaining the new lower bounds are useful for easy derivation of best unbiased predictors, which we illustrate with some examples.     

Functional equations in characterizations of discrete distributions ev rao-rubin condition and its variants

The solutions of Cauchy functional equation and its special cases, studied by various authors while characterizing discrete distributions by Rao-Rubin condition and its variants, axe discussed in this survey paper. Certain new results on the solutions of generalizations of these functional equations are also mentioned     

A Comparative Study of Some Modified Chi-Squared Tests

Some recent results in the theory and applications of modified chi-squared goodness-of-fit tests are briefly discussed. It seems that for the first time power of modified chi-squared type tests for the logistic and three-parameter Weibull distributions based on moment type estimators is studied. Power of different modified tests against some alternatives for equiprobable fixed or random grouping intervals, and for Neyman–Pearson classes is investigated. It is shown that power of test statistic essentially depends on the quantity of Fisher's sample information this statistic uses. Some recommendations on implementing modified chi-squared type tests are given.     

Robust quasi-randomization-based estimation with ensemble learning for missing data

Missing data analysis requires assumptions about an outcome model or a response probability model to adjust for potential bias due to nonresponse. Doubly robust (DR) estimators are consistent if at least one of the models is correctly specified. Multiply robust (MR) estimators extend DR estimators by allowing for multiple models for both the outcome and/or response probability models and are consistent if at least one of the multiple models is correctly specified. We propose a robust quasi-randomization-based model approach to bring more protection against model misspecification than the existing DR and MR estimators, where any multiple semiparametric, nonparametric or machine learning models can be used for the outcome variable. The proposed estimator achieves unbiasedness by using a subsampling Rao–Blackwell method, given cell-homogenous response, regardless of any working models for the outcome. An unbiased variance estimation formula is proposed, which does not use any replicate jackknife or bootstrap methods. A simulation study shows that our proposed method outperforms the existing multiply robust estimators.