A Well-Rounded Curriculum in Statistics

Reprinted by special permission of “The Iron Age”, this article describes how the statistical method used in control of product quality can be used as a technique for the control of accidents. Preliminary studies of this new approach indicate that it will aid materially in reducing accident rates, the authors declare.     

Nonparametric test for the homogeneity of the overall variability

In this paper, we propose a nonparametric test for homogeneity of overall variabilities for two multi-dimensional populations. Comparisons between the proposed nonparametric procedure and the asymptotic parametric procedure and a permutation test based on standardized generalized variances are made when the underlying populations are multivariate normal. We also study the performance of these test procedures when the underlying populations are non-normal. We observe that the nonparametric procedure and the permutation test based on standardized generalized variances are not as powerful as the asymptotic parametric test under normality. However, they are reliable and powerful tests for comparing overall variability under other multivariate distributions such as the multivariate Cauchy, the multivariate Pareto and the multivariate exponential distributions, even with small sample sizes. A Monte Carlo simulation study is used to evaluate the performance of the proposed procedures. An example from an educational study is used to illustrate the proposed nonparametric test.     

关系资产与中非间贸易:基于40国面板数据的实证研究

中非间长期友好关系是否产生贸易促进效应是双方外交关系可持续性及各自应对外部冲击能力的重要支撑，基于中非间较同质化的外交关系资产背景，通过引入弱惩罚和强惩罚机制的关系持续期和以外交关系等级衡量的投资强度变量来测度关系资产，以克服外交活动与贸易间存在的内生性问题，并纳入冲突力对中非间关系的影响，并利用2001～2017年非洲40国贸易数据构建面板校正误差模型，考察中非国家间关系资产对双边贸易及细分初级产品和制成品贸易是否存在促进效应。研究表明，关系资产对中非贸易有显著促进作用，但存在两个相反的关系资产对贸易影响机制，即关系持续期作为非纯公共产品的贸易促进作用和对较大经济规模国家的贸易摊薄效应；中国经济增长对中非双向出口贸易有较强带动作用，对非洲国家关税减免政策具有互惠特征，对中非双边贸易均有明显促进作用，但对不同细分品类具有差异化影响；中国和非洲国家应合力提升关系投资强度，以进一步发挥惯性力和国家间关系的贸易提升力作用，以贸易促进支撑中非全面战略合作伙伴关系的发展。     

Lad for Multiway Tables

It is shown that transformations based on differencing can be helpful in simplifying the problem of fitting to multiway tables. This is illustrated for LAD fitting, and the computational problems surveyed briefly.     

Model misspecification in parametric dual modeling

In typical normal theory regression, the assumption of homogeneity of variances is often not appropriate. Instead of treating the variances as a nuisance and transforming away the heterogeneity, the structure of the variances may be of interest and it is desirable to model the variances. Simultaneous modeling of the mean and variance of a response is known as dual modeling. When parametric models for the mean and variance are prescribed, estimation of the mean and variance parameters are interrelated. One commonly used dual model assumes a linear model for the mean and a log-linear variance model (Aitkin, 1987). This paper considers the impact of model misspecification (mean and variance) on the dual model estimation procedure. Asymptotic expressions for the mean and variance estimates, graphical illustrations of the impact of model misspecification, and simulation results are presented.     

Component reduction in linear discriminant analysis

The linear discriminant function is transformed into a linear combination of independent random variables. It is shown that reducing dimensionality using the smallest distance criterion results in smaller increase in the error rate than using the smallest variance criterion. Three error rates are used to prove this.     

Estimation of nonlinear simulation metamodels using control variates

The method of control variates has been intensively used for reducing the variance of estimated (linear) regression metamodels in simulation experiments. In contrast to previous studies, this article presents a procedure for applying multiple control variates when the objective is to estimate and validate a nonlinear regression metamodel for a single response, in terms of selected decision variables. This procedure includes robust statistical regression techniques for estimation and validation. Assuming joint normality of the response and controls, confidence intervals and hypothesis tests for the metamodel parameters are obtained. Finally, results for measuring the efficiency of the use of control variates are discussed.     

Some small-sample properties of some recently proposed multivariate outlier detection techniques

Recently, several new robust multivariate estimators of location and scatter have been proposed that provide new and improved methods for detecting multivariate outliers. But for small sample sizes, there are no results on how these new multivariate outlier detection techniques compare in terms of p _n , their outside rate per observation (the expected proportion of points declared outliers) under normality. And there are no results comparing their ability to detect truly unusual points based on the model that generated the data. Moreover, there are no results comparing these methods to two fairly new techniques that do not rely on some robust covariance matrix. It is found that for an approach based on the orthogonal Gnanadesikan–Kettenring estimator, p _n can be very unsatisfactory with small sample sizes, but a simple modification gives much more satisfactory results. Similar problems were found when using the median ball algorithm, but a modification proved to be unsatisfactory. The translated-biweights (TBS) estimator generally performs well with a sample size of n≥20 and when dealing with p-variate data where p≤5. But with p=8 it can be unsatisfactory, even with n=200. A projection method as well the minimum generalized variance method generally perform best, but with p≤5 conditions where the TBS method is preferable are described. In terms of detecting truly unusual points, the methods can differ substantially depending on where the outliers happen to be, the number of outliers present, and the correlations among the variables.     

On familial Poisson mixed models with multi-dimensional random effects

When a generalized linear mixed model with multiple (two or more) sources of random effects is considered, the inferences may vary depending on the nature of the random effects. In this paper, we consider a familial Poisson mixed model where each of the count responses of a family are influenced by two independent unobservable familial random effects with two distinct components of dispersion. A generalized quasilikelihood (GQL) approach is discussed for the estimation of the dispersion components as well as the regression effects of the model. A simulation study is conducted to examine the relative performance of the GQL approach as opposed to a simpler method of moments. Furthermore, the GQL estimation methodology is illustrated by using health care utilization data that follow a Poisson mixed model with one component of dispersion and by using simulated asthma data that follow a Poisson mixed model with two sources of random effects with two distinct components of dispersion.     

A simple bootstrap bandwidth selector for local polynomial fitting

A new, fully data-driven bandwidth selector with a double smoothing (DS) bias term and a data-driven variance estimator is developed following the bootstrap idea. The data-driven variance estimation does not involve any additional bandwidth selection. The proposed bandwidth selector convergences faster than a plug-in one due to the DS bias estimate, whereas the data-driven variance improves its finite sample performance clearly and makes it stable. Asymptotic results of the proposals are obtained. A comparative simulation study was done to show the overall gains and the gains obtained by improving either the bias term or the variance estimate, respectively. It is shown that the use of a good variance estimator is more important when the sample size is relatively small.