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     

Estimating E-bayesian and hierarchical bayesian of scalar parameter of gompertz distribution under type II censoring schemes based on fuzzy data

In this study, the E-Bayesian and hierarchical Bayesian of the scalar parameter of a Gompertz distribution under Type II censoring schemes were estimated based on fuzzy data under the squared error (SE) loss function and the efficiency of the proposed methods was compared with each other and with the Bayesian estimator using Monte Carlo simulation.     

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.     

基于“3R＆I”原则的循环经济模式研究

我国当前经济高速增长的要求与有限资源和环境支持能力之间存在严重矛盾。实施循环经济是贯彻落实我国节能减排政策的有效途径,如何发展循环经济是我们面临的重大课题。目前循环经济的实施主要是依据“3R”原则,而这些原则有明显的不足之处。针对“3R”原则的局限性,提出基于创新的循环经济“3R＆I”原则。创新是实现“减量化”、“再利用”、“资源化”的前提,也是实现经济持续循环的保证。循环经济本质上是一种创新经济。     

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。     

用牛顿环实验测量凸透镜曲率半径的误差分析

对牛顿环测量凸透镜曲率半径实验中的误差进行了理论分析和半定量分析,指出了误差的主要来源及相应的处理方法.对于测量曲率半径P>lm的平凸透镜,公式R=Dm2-Dn2/4（m-n）λ的理论相对误差小于10-8;逐差法可以消除形变带来的系统误差;由于形变的影响应从第5级以后开始计数,对于R>1m的凸透镜要得到小于10-3的相对误差,级数应小于50,级数差值应大于30.钠光灯作为光源的系统相对误差为7.1×10-4.