Noninformative priors for the between-group variance in the unbalanced one-way random effects model with heterogeneous error variances

For the unbalanced one-way random effects model with heterogeneous error variances, we propose the non-informative priors for the between-group variance and develop the first- and second-order matching priors. It turns out that the second-order matching priors do not exist and the reference prior and Jeffreys prior do not satisfy a first-order matching criterion. We also show that the first-order matching prior meets the frequentist target coverage probabilities much better than the Jeffreys prior and reference prior through simulation study, and the Bayesian credible intervals based on the matching prior and reference prior give shorter intervals than the existing confidence intervals by examples.     

On Bartlett correction of empirical likelihood for regularly spaced spatial data

Bartlett correction constitutes one of the attractive features of empirical likelihood because it enables the construction of confidence regions for parameters with improved coverage probabilities. We study the Bartlett correction of spatial frequency domain empirical likelihood (SFDEL) based on general spectral estimating functions for regularly spaced spatial data. This general formulation can be applied to testing and estimation problems in spatial analysis, for example testing covariance isotropy, testing covariance separability as well as estimating the parameters of spatial covariance models. We show that the SFDEL is Bartlett correctable. In particular, the improvement in coverage accuracies of the Bartlett‐corrected confidence regions depends on the underlying spatial structures. The Canadian Journal of Statistics 47: 455–472; 2019 © 2019 Statistical Society of Canada     

Generalized estimator of population mean by using conventional and non-conventional measures in the presence of measurement errors

In survey research, it is assumed that reported response by the individual is correct. However, given the issues of prestige bias, self-respect, respondent's reported data often produces estimated values which are highly deviated from the true values. This causes measurement error (ME) to be present in the sample estimates. In this article, the estimation of population mean in the presence of measurement error using information on a single auxiliary variable is studied. A generalized estimator of population mean is proposed. The class of estimators is obtained by using some conventional and non-conventional measures. Simulation and numerical study is also conducted to assess the performance of estimators in the presence and absence of measurement error.     

The effect of small sample on optimal designs for logistic regression models

Asymptotic methods are commonly used in statistical inference for unknown parameters in binary data models. These methods are based on large sample theory, a condition which may be in conflict with small sample size and hence leads to poor results in the optimal designs theory. In this paper, we apply the second order expansions of the maximum likelihood estimator and derive a matrix formula for the mean square error (MSE) to obtain more precise optimal designs based on the MSE. Numerical results indicate the new optimal designs are more efficient than the optimal designs based on the information matrix.     

MSE performance of the weighted average estimators consisting of shrinkage estimators when each individual regression coefficient is estimated

In this paper, we analytically derive the exact formula for the mean squared error (MSE) of two weighted average (WA) estimators for each individual regression coefficient. Further, we execute numerical evaluations to investigate small sample properties of the WA estimators, and compare the MSE performance of the WA estimators with the other shrinkage estimators and the usual OLS estimator. Our numerical results show that (1) the WA estimators have smaller MSE than the other shrinkage estimators and the OLS estimator over a wide region of parameter space; (2) the range where the relative MSE of the WA estimator is smaller than that of the OLS estimator gets narrower as the number of explanatory variables k increases.     

Non-parametric estimation of reciprocal coordinate subtangent for right censored dependent scheme

The concept of reciprocal coordinate subtangent (RCST) has been used as a useful tool to study the monotone behavior of a continuous density function and for characterizing probability distributions. In this paper, we propose a non-parametric estimator for RCST based on the censored dependent data. Asymptotic properties of the estimator are established under suitable regularity conditions. A simulation study is carried out to examine the performance of the estimator. The usefulness of the estimator is also examined through a real data.     

The laws of large numbers for Pareto-type random variables with infinite means

In this paper, we consider the laws of large numbers for NSD random variables satisfying Pareto-type distributions with infinite means. Based on the Pareto-Zipf distributions, some weak laws of large numbers for weighted sums of NSD random variables are obtained. Meanwhile, we show that a weak law for Pareto-Zipf distributions cannot be extended to a strong law. Furthermore, based on the two tailed Pareto distribution, a strong law of large numbers for weighed NSD random variables is presented. Our results extend the corresponding earlier ones.     

多阶段均值—半方差模糊投资组合决策研究

考虑交易成本、借款限制、阀值约束和基数约束,提出多阶段均值—半方差模糊投资组合模型。在该模型中,收益水平被定义为可能的平均回报,风险水平被定义为回报的半方差。由于交易成本和基数约束,多阶段投资组合模型为具有路径依赖性的混合整数动态优化问题。文章提出了前向动态规划方法求解。最后,以一个具体的算例比较了不同的基数约束投资组合的最优投资策略。     

固定资产投资与国内生产总值的误差修正模型研究

运用协整理论和误差修正模型研究固定资产投资和国内生产总值之间的关系,可以发现它们之间存在长期均衡的协整关系,使用误差修正模型比普通的单变量方程更能反映两者长期和短期的关系,还可以避免谬误回归问题。     

孔子通才教育观简论

孔子是中国传统教育理论的创立者,至今仍有重要影响。二千五百年来,孔子的思想对中国文化和中国思想产生了深远的影响。文章拟从他关于仁爱、中庸和慎言等教育思想中,揭示其通才教育观的基本内容,为现行素质教育作参考。研究孔子思想有重要的现实意义。