Small sample size comparisons of tests for homogeneity of variances by Monte-Carlo

A number of tests are available for testing the equality of several population variances. Some are claimed to be robust. We compared six of those claimed robust procedures by Monte Carlo simulated experiments, particularly for cases of small and unequal sample sizes. Our results show that the jack-knife test compares favorably with the other tests.     

Estimation in Varying-Coefficient Errors-in-Variables Models with Missing Response Variables

This article is concerned with the estimation of a varying-coefficient regression model when the response variable is sometimes missing and some of the covariates are measured with additive errors. We propose a class of estimators for the coefficient functions, as well as for the population mean and the error variance. The resulting estimators are shown to be asymptotically normal. Simulation studies are conducted to illustrate our approach.     

Selection of the Ridge Parameter Using Mathematical Programming

Ridge regression solves multicollinearity problems by introducing a biasing parameter that is called ridge parameter; it shrinks the estimates and their standard errors in order to reach acceptable results. Selection of the ridge parameter was done using several subjective and objective techniques that are concerned with certain criteria. In this study, selection of the ridge parameter depends on other important statistical measures to reach a better value of the ridge parameter. The proposed ridge parameter selection technique depends on a mathematical programming model and the results are evaluated using a simulation study. The performance of the proposed method is good when the error variance is greater than or equal to one; the sample consists of 20 observations, the number of explanatory variables in the model is 2, and there is a very strong correlation between the two explanatory variables.     

Non-Diagonal-Type Estimator in Linear Regression

This short article mainly aims to introduce the notion of the non-diagonal-type estimator (NDTE) by means of the singular value decomposition theorem in the linear regression model to improve some classical linear estimators that can be called the diagonal-type estimators. We derive the optimal NDTE under the mean squared error criterion and its iterative version through matrix techniques. A simulation study is finally conducted to illustrate the theoretical results.     

The Synthetic Mean Square Error Control Chart

A synthetic mean square error (MSE) control chart is presented in this study for monitoring the changes in the mean and standard deviation of a normally distributed process. The synthetic MSE control chart is a combination of the standard MSE control chart and the conforming run length (CRL) control chart. From the numerical comparisons, the synthetic MSE control chart is always more efficient than the standard MSE control chart in detecting shifts in the process mean and standard deviation. The synthetic MSE chart also performs better than the exponentially weighted moving average-semicircle (EWMA-SC) chart, except for some cases where the process mean shifts are small.     

Bayesian Statistical Inference for Weighted Exponential Distribution

Exponential distribution has an extensive application in reliability. Introducing shape parameter to this distribution have produced various distribution functions. In their study in 2009, Gupta and Kundu brought another distribution function using Azzalini's method, which is applicable in reliability and named as weighted exponential (WE) distribution. The parameters of this distribution function have been recently estimated by the above two authors in classical statistics. In this paper, Bayesian estimates of the parameters are derived. To achieve this purpose we use Lindley's approximation method for the integrals that cannot be solved in closed form. Furthermore, a Gibbs sampling procedure is used to draw Markov chain Monte Carlo samples from the posterior distribution indirectly and then the Bayes estimates of parameters are derived. The estimation of reliability and hazard functions are also discussed. At the end of the paper, some comparisons between classical and Bayesian estimation methods are studied by using Monte Carlo simulation study. The simulation study incorporates complete and Type-II censored samples.     

A Study on the Robustness of G-Chart to Non-Normality

The G-chart is proposed by Riaz and Saghirr (2007 Riaz, M., Saghirr, A. (2007). Monitoring Process Variability using Gini's mean difference. Quality Technology and Quantitative Management 4:439–454.[Taylor & Francis Online] , [Google Scholar]) for monitoring the changes in the process variability more efficiently. This study investigates the influence of the parent population on the coefficients of the G-Chart. The appropriate values of the coefficients (b₂ and b₃) has been determined when the distributions of the processes are the normal, exponential, uniform, Laplace, and triangular. The false alarm rate and risk of type II error as performance measures of the G-chart are obtained. The robustness of the G-chart relative to Q- and R_Q-charts is studied. The efficiency of the G-chart relative to those of R-chart for detecting a shift in the process dispersion is examined. The results reveal that the proper attention to the parent population leads to the better performances of the G-chart. The G-chart is more robust than Q-chart and is slightly less efficient than R_Q-chart for detecting outliers. The G-chart is more efficient than R-chart to detect a shift for normal and non-normal processes.     

The effect of temporal aggregation on the estimation accuracy of ARMA models

ABSTRACT

Autoregressive Moving Average (ARMA) time series model fitting is a procedure often based on aggregate data, where parameter estimation plays a key role. Therefore, we analyze the effect of temporal aggregation on the accuracy of parameter estimation of mixed ARMA and MA models. We derive the expressions required to compute the parameter values of the aggregate models as functions of the basic model parameters in order to compare their estimation accuracy. To this end, a simulation experiment shows that aggregation causes a severe accuracy loss that increases with the order of aggregation, leading to poor accuracy.     

中国信息产业与经济增长关系实证分析

根据协整理论,利用1991—2007年经济数据对中国信息产业和经济增长的关系进行实证分析,测算该时间跨度信息产业对经济增长的长期和短期弹性,基于ECM检验两者之间是否存在格兰杰因果关系,最后利用广义脉冲响应函数描述两者的互动关系。     

03版高中文言文文意注释辨析

文言文注释是中学语文教材注释的重要组成部分,同时也是中学语文教材注释的难点和重点。课文注释是中学生阅读文言文必不可少的辅助资料。因此,其质量高低直接影响到文言文教学的效果。然而2003年秋季发行的新版高中语文教材(人民教育出版社)中文言文中文意注释方面却存在着砂谬误。