Density estimation in the uniform deconvolution model

We consider the problem of estimating a probability density function based on data that are corrupted by noise from a uniform distribution. The (nonparametric) maximum likelihood estimator for the corresponding distribution function is well defined. For the density function this is not the case. We study two nonparametric estimators for this density. The first is a type of kernel density estimate based on the empirical distribution function of the observable data. The second is a kernel density estimate based on the MLE of the distribution function of the unobservable (uncorrupted) data.     

对小地区失业统计差额比的推定

本文对韩国国内行政区域如市郡区等小地区的失业统计共同差额比进行推定的方法有联合推定量,Woolf推定量和Mantel-Haenszel推定量等。对这个推定量的可信度是通过偏差和平均平方误差的概念来进行比较的。从对京畿地区经济活动人口调查情况看,这个地区内的24个市郡单位行政自治地区的男、女失业率差额比的偏差及平均平方误差是通过本次研究提出的推定程序来推定的。这些推定数的稳定性和效率性可以通过相对偏差和相对平均误差平方根来评价。Woolf推定量或Mantel-Haenszel推定量比联合推定量更为稳定,从其效率性来看三者很相似。     

On Testing for the Nullity of Some Skewness Coefficients

Three tests for the skewness of an unknown distribution are derived for iid data. They are based on suitable normalization of estimators of some usual skewness coefficients. Their asymptotic null distributions are derived. The tests are next shown to be consistent and their power under some sequences of local alternatives is investigated. Their finite sample properties are also studied through a simulation experiment, and compared to those of the √ b ₂-test.     

On efficiency of the ratio estimator

Summary The exact mean square error for the ratio estimator of a finite population total based on simple random sampling without replacement is shown to have an expected value less than that of the variance of the ratio estimator based on Midzuno’s scheme, under a usual super-population model.     

Locally minimum variance unbiased estimator in a discontinuous density function

The exact forms of the locally minimum variance unbiased estimators and their variances are given in the case of a discontinuous density function.     

Pseudo empirical likelihood method in the presence of missing data

In this paper, we propose an estimator for the population mean when some observations on the study and auxiliary variables are missing from the sample. The proposed estimator is valid for any unequal probability sampling design, and is based upon the pseudo empirical likelihood method. The proposed estimator is compared with other estimators in a simulation study.     

Asymptotic behaviour of regression pre-test estimators with minimal Bayes risk

Pre-test estimators (PTE) are considered which are optimal under a Bayes risk among PTE with general measurable sets as “regions of significance” for the test statistic t associated with the estimate of a given regression coefficient. Asymptotic and some finite sample results are stated and numerical experiments are commented on.     

Modelling of repairable systems with various degrees of repair

The availability of a stochastic repairable system depends on the failure behaviour and on repair strategies. In this paper, we deal with a general repair model for a system using auxiliary counting processes and corresponding intensities which include various degrees of repair (between minimal repair and perfect repair). For determining the model parameters we need estimators depending on failure times and repair times: maximum likelihood (ML) estimator and Bayes estimators are considered. Special results are obtained by the use of Weibull-type intensities and random observation times.     

Some properties of the length of the shortest half

This paper discusses some properties of the length of the shortest half proposed by Rousseeuw and Leroy (1988) as a robust scale estimator.