Logistic discrimination using robust estimators: An influence function approach

Logistic regression is frequently used for classifying observations into two groups. Unfortunately there are often outlying observations in a data set and these might affect the estimated model and the associated classification error rate. In this paper, the authors study the effect of observations in the training sample on the error rate by deriving influence functions. They obtain a general expression for the influence function of the error rate, and they compute it for the maximum likelihood estimator as well as for several robust logistic discrimination procedures. Besides being of interest in their own right, the influence functions are also used to derive asymptotic classification efficiencies of different logistic discrimination rules. The authors also show how influential points can be detected by means of a diagnostic plot based on the values of the influence function     

零起点阿拉伯语专业学生常见写作错误分析

外语教学中的"语言错误"常常困扰教者与学者。本文根据错误理论及错误分析的观点,对零起点阿拉伯语专业学生在语言习得中出现的语言错误进行了归纳与总结,提出了解决这些难题的方法。     

Prediction Error Estimation Under Bregman Divergence for Non-Parametric Regression and Classification

Abstract.  Prediction error is critical to assess model fit and evaluate model prediction. We propose the cross-validation (CV) and approximated CV methods for estimating prediction error under the Bregman divergence (BD), which embeds nearly all of the commonly used loss functions in the regression, classification procedures and machine learning literature. The approximated CV formulas are analytically derived, which facilitate fast estimation of prediction error under BD. We then study a data-driven optimal bandwidth selector for local-likelihood estimation that minimizes the overall prediction error or equivalently the covariance penalty. It is shown that the covariance penalty and CV methods converge to the same mean-prediction-error-criterion. We also propose a lower-bound scheme for computing the local logistic regression estimates and demonstrate that the algorithm monotonically enhances the target local likelihood and converges. The idea and methods are extended to the generalized varying-coefficient models and additive models.     

A modified estimator of population mean using power transformation

Summary In this paper we have suggested two modified estimators of population mean using power transformation. It has been shown that the modified estimators are more efficient than the sample mean estimator, usual ratio estimator, Sisodia and Dwivedi’s (1981) estimator and Upadhyaya and Singh’s (1999) estimator at their optimum conditions. Empirical illustrations are also given for examining the merits of the proposed estimators. Following Kadilar and Cingi (2003) the work has been extended to stratified random sampling, and the same data set has been studied to examine the performance in stratified random sampling.     

A general class of chain estimators for ratio and product of two means of a finite population

This paper proposes a class of estimators for estimating ratio and product of two means of a finite population using information on two auxiliary characters. Asymptotic expression to terms of order 0(n^-1) for bias and mean square error (MSE) of the proposed class of estimators are derived. Optimum conditions are obtained under which the proposed class of estimators has the minimum MSE. An empirical study is carried out to compare the performance of various estimators of ratio with the conventional estimators.     

Inference for Variance Components in a Mixed Model for Unbalanced Split Plot Design

Abstract

We consider the unbalanced split-plot design with the whole plot and the subplot effect from nonnormal universes. The three estimators for the whole plot effect variance component are obtained. An approximate test for significance of the whole plot effect variance component is presented.     

Estimation method of multivariate exponential probabilities based on a simplex coordinates transform

A novel unbiased estimator for estimating the probability mass of a multivariate exponential distribution over a measurable set is introduced and is called the exponential simplex (ES) estimator. For any measurable set and given sample size, the statistical efficiency of the ES estimator is higher than or equal to the statistical efficiency of the well-known Monte Carlo (MC) estimator. For non-radially shaped measurable sets, the ES estimator has a strictly higher statistical efficiency than the MC estimator. For ray-convex sets, such as convex sets, the ES estimator can be expressed in a simple analytical form.     

Application of box-cox transformations to discrimination for the two-class problem

The performance of Box-Cox power transformations in classification using Hinkley's (1975) method is studied. Misclassification probabilities before and after transformation are compared. It is found that the use of Box-Cox transformations can sometimes substantially reduce the error probabilities. Estimates of error probabilities are obtained and certain properties are derived. Examples for a number of distributions are given.     

Effect of the sample on the posterior probability in bayesian analysis

This paper examines Bayesian posterior probabilities as a function of selected elements within the set of data, x, when the prior distribution is assumed fixed. The posterior probabilities considered here are those of the parameter vector lying in a subset of the total parameter space. The theorems of this paper provide insight into the effect of elements within x on this posterior probability. These results have applications, for example, in the study of the impact of outliers within the data and in the isolation of misspecified parameters in a model.     

我国短期债券回购利率与同业拆借利率的协整分析

本文利用协整检验的相关理论，对我国银行间短期债券回购利率和同业拆借利率的关系进行了探讨。结果显示，我国银行间短期国债回购利率和同业拆借市场利率之间存在长期均衡关系。此外，文章还利用误差修正模型，分析了国债回购利率和同业拆借利率之间的短期波动。