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.     

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.     

货运与经济发展协整关系的实证分析

应用协整方法研究我国交通运输系统规模与宏观经济发展之间的动态关联,对于把握交通系统的发展方向,合理规划交通系统,并使其与经济的发展相适应,具有重要意义。应用协整方法分析、检验了我国货运规模与经济发展之间的协整关系,定量分析了主要相关因素对货运发展的影响,建立了描述货运周转量由短期波动向长期均衡调整的动态过程的误差修正模型。分析结果表明,我国货运周转量与工业生产总值和运价之间存在唯一的长期稳定关系,短期预测模型不仅具有令人满意的拟合效果和预测能力,而且结构具有稳定性。     

中国创新活动和经济增长的关系——一个基于协整理论的初步研究

内生经济增长理论告诉我们,创新活动作为技术进步的主要来源能够持续推动经济增长。但是中国现阶段经济发展条件下创新对经济增长的推动作用到底有多大,创新活动对于经济增长的影响机制如何,现有的研究并没有给出一个令人信服的答案。本文采用协整理论和误差修正模型研究了经济增长和创新活动之间的关系。研究结果显示,我国创新活动对于经济增长短期内具有显著影响,但其影响程度与长期影响相比还存在着较大差距;从长期看各种创新活动中基础研究能够实现对经济增长更大的推动作用。