Conditional inference in finite population sampling under a calibration model

Several estimators, including the classical and the regression estimators of finite population mean, are compared, both theoretically and empirically, under a calibration model, where the dependent variable(y), and not the independent variable(x), can be observed for all units of the finite population. It is shown asymptotically that when conditioned on x, the bias of the classical estimator may be much smaller than that of the regression estimators; whereas when conditioned on y, the regression estimator may have much smaller conditional bias than the classical estimator. Since all the y's(not x's) can be observed, it seems appropriate to make comparison under the conditional distribution of each estimator with y fixed. In this case, the regression estimator has smaller variance, smaller conditional bias, and the conditional coverage probability closer to its nominal level     

Restricted Estimation in Partially Linear Errors-in-Variables Models

As a compromise between parametric regression and nonparametric regression, partially linear models are frequently used in statistical modelling. This article considers statistical inference for this semiparametric model when the linear covariate is measured with additive error and some additional linear restrictions on the parametric component are assumed to hold. We propose a restricted corrected profile least-squares estimator for the parametric component, and study the asymptotic normality of the estimator. To test hypothesis on the parametric component, we construct a Wald test statistic and obtain its limiting distribution. Some simulation studies are conducted to illustrate our approaches.     

关于极限的求解方略

极限是研究高等数学的重要工具，其求解方法千变万化，而一般的教材仅能介绍一些主要方法，且缺少系统性，本文试从多种角度和方式来研究和总结极限的求解方法．     

Estimation of location parameters of several exponential distributions

In this paper we address the problem of simultaneous estimation of location parameters of several exponential distributions assuming that the scale parameters are unknown and possibly unequal. From a decision theoretic point of view it is shown that the standard estimators are inadmissible and the improved estimators are obtained when p, the number of populations, is more than one.     

Estimating capability index cpk for processes with asymmetric tolerances

Pearn and Chen (1996) considered the process capability index C_pk, and investigated the statistical properties of its natural estimator under various process conditions. Their investigation, however, was restricted to processes with symmetric tolerances. Recently, Pearn and Chen (1998) considered a generalization of C_pk, referred to as C^? _pk, to cover processes with asymmetric tolerances. They investigated the statistical properties of the natural estimator of C^? _pk, and obtained the exact formulae for the expected value and variance. In this paper, we consider a new estimator of C^? _pk, assuming the knowledge on P(LI > T) = p is available, where 0 > p > 1, which can be obtained from historical information of a stable process. We obtain the exact distribution of the new estimator assuming the process characteristic follows the normal distribution. We show that the new estimator is consistent, asymptotically unbiased, which converges to a mixture of two normal distributions. We also show that by adding suitable correction factors to the new estimator, we may obtain the UMVUE and the MLE of the generalization C^? _pk.     

Frame Correction Modelling with Applications to the German Register‐Assisted Census 2011

Frame corrections have been studied in census applications for a long time. One very promising method is dual system estimation, which is based on capture–recapture models. These methods have been applied recently in the USA, England, Israel and Switzerland. In order to gain information on subgroups of the population, structure preserving estimators can be applied [i.e. structure preserving estimation (SPREE) and generalized SPREE]. The present paper extends the SPREE approach with an alternative distance function, the chi‐square. The new method has shown improved estimates in our application with very small domains. A comparative study based on a large‐scale Monte Carlo simulation elaborates on advantages and disadvantages of the estimators in the context of the German register‐assisted Census 2011.     

On tail index estimation based on multivariate data

This article is devoted to the study of tail index estimation based on i.i.d. multivariate observations, drawn from a standard heavy-tailed distribution, that is, of which Pareto-like marginals share the same tail index. A multivariate central limit theorem for a random vector, whose components correspond to (possibly dependent) Hill estimators of the common tail index α, is established under mild conditions. We introduce the concept of (standard) heavy-tailed random vector of tail index α and show how this limit result can be used in order to build an estimator of α with small asymptotic mean squared error, through a proper convex linear combination of the coordinates. Beyond asymptotic results, simulation experiments illustrating the relevance of the approach promoted are also presented.     

Interval estimation of the negative binomial dispersion parameter

Inference concerning the negative binomial dispersion parameter, denoted by c, is important in many biological and biomedical investigations. Properties of the maximum-likelihood estimator of c and its bias-corrected version have been studied extensively, mainly, in terms of bias and efficiency [W.W. Piegorsch, Maximum likelihood estimation for the negative binomial dispersion parameter, Biometrics 46 (1990), pp. 863–867; S.J. Clark and J.N. Perry, Estimation of the negative binomial parameter κ by maximum quasi-likelihood, Biometrics 45 (1989), pp. 309–316; K.K. Saha and S.R. Paul, Bias corrected maximum likelihood estimator of the negative binomial dispersion parameter, Biometrics 61 (2005), pp. 179–185]. However, not much work has been done on the construction of confidence intervals (C.I.s) for c. The purpose of this paper is to study the behaviour of some C.I. procedures for c. We study, by simulations, three Wald type C.I. procedures based on the asymptotic distribution of the method of moments estimate (mme), the maximum-likelihood estimate (mle) and the bias-corrected mle (bcmle) [K.K. Saha and S.R. Paul, Bias corrected maximum likelihood estimator of the negative binomial dispersion parameter, Biometrics 61 (2005), pp. 179–185] of c. All three methods show serious under-coverage. We further study parametric bootstrap procedures based on these estimates of c, which significantly improve the coverage probabilities. The bootstrap C.I.s based on the mle (Boot-MLE method) and the bcmle (Boot-BCM method) have coverages that are significantly better (empirical coverage close to the nominal coverage) than the corresponding bootstrap C.I. based on the mme, especially for small sample size and highly over-dispersed data. However, simulation results on lengths of the C.I.s show evidence that all three bootstrap procedures have larger average coverage lengths. Therefore, for practical data analysis, the bootstrap C.I. Boot-MLE or Boot-BCM should be used, although Boot-MLE method seems to be preferable over the Boot-BCM method in terms of both coverage and length. Furthermore, Boot-MLE needs less computation than Boot-BCM.     

A Convolution Estimator for the Density of Nonlinear Regression Observations

Abstract. The problem of estimating an unknown density function has been widely studied. In this article, we present a convolution estimator for the density of the responses in a nonlinear heterogenous regression model. The rate of convergence for the mean square error of the convolution estimator is of order n ^?1 under certain regularity conditions. This is faster than the rate for the kernel density method. We derive explicit expressions for the asymptotic variance and the bias of the new estimator, and further a data‐driven bandwidth selector is proposed. We conduct simulation experiments to check the finite sample properties, and the convolution estimator performs substantially better than the kernel density estimator for well‐behaved noise densities.     

Public relations functions: Perspective from a Japanese corporation

This paper examines public relations (PR) functions in a large Japanese corporation as well as the PR role in the management function. The corporation under study is Kao Corporation, which is one of the largest Japanese consumer and industrial goods manufacturers. Information was collected from interviewing a PR manager of Kao Corporation. Evidence suggests that Kao's PR department functions more or less like an advertising department. Press releases are placed in the media as paid advertisements. Kao's PR uses a third-party endorsement to establish a new product's credibility. The company has a participative corporate culture that allows the PR director to work closely with the top management. The idea of collaborative efforts between departments and the practice of being a socially responsible company suggest that Kao's PR department uses a combination of communication models and Japanese management styles to project a good corporate citizen image.