Bayesian estimation for the Pareto income distribution

The Bayes estimators of the Gini index, the mean income and the proportion of the population living below a prescribed income level are obtained in this paper on the basis of censored income data from a pareto income distribution. The said estimators are obtained under the assumptions of a two-parameter exponential prior distribution and the usual squared error loss function. This work is also extended to the case when the income data are grouped and the exact incomes for the individuals in the population are not available. The method for the assessment of the hyperparameters is also outlined. Finally, the results are generalized for the doubly truncated gamma prior distribution. Now deceased.     

Multiple roots of estimating functions

Estimating functions can have multiple roots. In such cases, the statistician must choose among the roots to estimate the parameter. Standard asymptotic theory shows that in a wide variety of cases, there exists a unique consistent root, and that this root will lie asymptotically close to other consistent (possibly inefficient) estimators for the parameter. For this reason, attention has largely focused on the problem of selecting this root and determining its approximate asymptotic distribution. In this paper, however, we concentrate on the exact distribution of the roots as a random set. In particular, we propose the use of higher-order root intensity functions as a tool for examining the properties of the roots and determining their most problematic features. The use of root intensity functions of first and second order is illustrated by application to the score function for the Cauchy location model.     

关于Mobius函数的一些性质

Mobius 函数在近代数论上古着非常重要的应用.尤其在 Selberg 筛法中,更是起着几乎是决定性的作用.术文着重讨论 Mobius 变换的一些性质,并得出一些变换公式。     

极限证明初探

本文结合教学中正反两方面的例子,从理论上较深入地讨论了如何理解极限定义和掌握极限证明的方法,并回答了证明中可能出现的问题.     

从供应链分析探讨传统出口型外贸企业的发展战略

从分析传统外贸企业在国际供应链中的地位入手,研究了传统外贸企业的现有功能和功能扩展空间,从而提出传统外贸企业应该坚持加强供应链管理、加强战略合作伙伴关系的建设,并努力实现信息化的战略发展方向。     

Error rates in classification consisting of discrete and continuous variables in the presence of covariates

We consider classifying an object based on mixed continuous and discrete variables between two populations. Mixed discrete and continuous covariates with identical means in both populations are amongst the variables. Under the location model with homogeneous location specific conditional dispersion matrices for both populations, the Bayes rule is given. Classification is implemented by a plug-in version of the Bayes rule with full covariate adjustment. An asymptotic expansion of the overall expected error of the procedure is derived. Our findings generalize several classical results.     

Vector random fields with compactly supported covariance matrix functions

The objective of this paper is to construct covariance matrix functions whose entries are compactly supported, and to use them as building blocks to formulate other covariance matrix functions for second-order vector stochastic processes or random fields. In terms of the scale mixture of compactly supported covariance matrix functions, we derive a class of second-order vector stochastic processes on the real line whose direct and cross covariance functions are of Pólya type. Then some second-order vector random fields in R^d${\mathbb{R}}^d$ whose direct and cross covariance functions are compactly supported are constructed by using a convolution approach and a mixture approach.     

Nonparametric smooth estimation of the expected inactivity time function

The expected inactivity time (EIT) function (also known as the mean past lifetime function) is a well known reliability function which has application in many disciplines such as survival analysis, actuarial studies and forensic science, to name but a few. In this paper, we use a fixed design local polynomial fitting technique to obtain estimators for the EIT function when the lifetime random variable has an unknown distribution. It will be shown that the proposed estimators are asymptotically unbiased, consistent and also, when standardized, has an asymptotic normal distribution. An optimal bandwidth, which minimizes the AMISE (asymptotic mean integrated squared error) of the estimator, is derived. Numerical examples based on simulated samples from various lifetime distributions common in reliability studies will be presented to evaluate the performances of these estimators. Finally, three real life applications will also be presented to further illustrate the wide applicability of these estimators.     

Adaptive estimation of the conditional cumulative distribution function from current status data

Consider a positive random variable of interest Y depending on a covariate X, and a random observation time T independent of Y given X. Assume that the only knowledge available about Y is its current status at time T  : δ=_I{Y≤T}$\delta ={\mathbb{I}}_{\{Y\le T\}}$ with I$\mathbb{I}$ the indicator function. This paper presents a procedure to estimate the conditional cumulative distribution function F of Y given X   from an independent identically distributed sample of (X,T,δ)$(X,T,\delta )$.     

Robust estimation for ordinal regression

Ordinal regression is used for modelling an ordinal response variable as a function of some explanatory variables. The classical technique for estimating the unknown parameters of this model is Maximum Likelihood (ML). The lack of robustness of this estimator is formally shown by deriving its breakdown point and its influence function. To robustify the procedure, a weighting step is added to the Maximum Likelihood estimator, yielding an estimator with bounded influence function. We also show that the loss in efficiency due to the weighting step remains limited. A diagnostic plot based on the Weighted Maximum Likelihood estimator allows to detect outliers of different types in a single plot.