Product-limit Estimators and Cox Regression with Missing Censoring Information

The Kaplan–Meier estimator of a survival function requires that the censoring indicator is always observed. A method of survival function estimation is developed when the censoring indicators are missing completely at random (MCAR). The resulting estimator is a smooth functional of the Nelson–Aalen estimators of certain cumulative transition intensities. The asymptotic properties of this estimator are derived. A simulation study shows that the proposed estimator has greater efficiency than competing MCAR-based estimators. The approach is extended to the Cox model setting for the estimation of a conditional survival function given a covariate.     

Double Sampling Ratio-product Estimator of a Finite Population Mean in Sample Surveys

It is well known that two-phase (or double) sampling is of significant use in practice when the population parameter(s) (say, population mean X¯) of the auxiliary variate x is not known. Keeping this in view, we have suggested a class of ratio-product estimators in two-phase sampling with its properties. The asymptotically optimum estimators (AOEs) in the class are identified in two different cases with their variances. Conditions for the proposed estimator to be more efficient than the two-phase sampling ratio, product and mean per unit estimator are investigated. Comparison with single phase sampling is also discussed. An empirical study is carried out to demonstrate the efficiency of the suggested estimator over conventional estimators.     

Comparison of estimators of the location parameter using pitman's closeness criterion

Necessary and sufficient conditions for a linear estimator to dominate another linear estimator of a location parameter under the Pitman's criterion of comparison are discussed. Consequently it is demonstrated that a linear biased estimator can not dominate a linear unbiased estimator under Pitman's criterion and that the sample mean is the Closest Linear Unbiased Estimator (CLUE). It is also shown that the ridge regression estimator with a known biasing constant can not dominate the ordinary least squares estimator. If an estimator δdominates an estimator δin the average loss sense then sufficient conditions are obtained under which δis also preferred over δunder Pitman's criterion. Further we obtain sufficient conditions under which preference under the Pitman's criterion will lead to preference under the mean squared error sense.     

A Measure of partial association between disease and genotype for the two-parent problem

The two-parent disease-genotype association problem is studied from the point of view of a coefficient of association between the disease phenotype of the child and the disease phenotypes of the parents, in the presence of some genotypic information about the parents. This coefficient of partial association is derived, and certain tests of hypotheses are constructed. The results are shown to be useful in estimation of recurrence risks, and in understanding the nature of the association between child and parental disease phenotypes.     

On Robust Analysis of a Normal Location Parameter

Pericchi and Smith considered a normal location parameter problem with double-exponential and Student t prior distributions. These two prior distributions both belong to the class of scale mixtures of normal distributions and are useful in providing a robust analysis of the normal location parameter problem. In this paper we extend the analysis to other scale mixtures of normal distributions, such as the exponential power and the symmetric stable distributions.     

THE POWER OF STUDENT'S t TEST: CAN A NON-SIMILAR TEST DO BETTER?

Lehmann & Stein (1948) proved the existence of non-similar tests which can be more powerful than best similar tests. They used Student's problem of testing for a non-zero mean given a random sample from the normal distribution with unknown variance as an example. This raises the question: should we use a non-similar test instead of Student's t test? Questions like this can be answered by comparing the power of the test with the power envelope. This paper discusses the difficulties involved in computing power envelopes. It reports an empirical comparison of the power of the t test and the power envelope and finds that the two are almost identical especially for sample sizes greater than 20. These findings suggest that, as well as being uniformly most powerful (UMP) within the class of similar tests, Student's t test is approximately UMP within the class of all tests. For practical purposes it might also be regarded as UMP when moderate or large sample sizes are involved.     

涉外离婚准据法选择方法的发展新趋势及启示

自20世纪后半叶以来,为了解决旧的学说存在的缺陷问题,涉外离婚的准据法选择方面出现了一些新的趋势:适用有利于实现离婚的法律、引入“最密切联系原则”、引入“意思自治原则”。这些新的发展趋势对确立我国涉外离婚的准据法具有非常重要的借鉴作用。     

Influence diagnostics in the capital asset pricing model under elliptical distributions

In this paper we consider the Capital Asset Pricing Model under Elliptical (symmetric) Distributions. This class of distributions, which contains the normal distribution, t, contaminated normal and power exponential, among others, offers a more flexible framework for modelling asset prices or returns. In order to analyze the sensibility to possible outliers and/or atypical returns of the maximum likelihood estimators, the local influence method was implemented. The results are illustrated by using a set of shares from companies who trade in the Chilean Stock Market. Our main conclusion is that symmetric distributions having heavier tails than those of the normal distribution, especially the t distribution with small degrees of freedom, show a better fit and allow the reduction of the influence of atypical returns in the maximum likelihood estimators.     

Estimating the Upper Support Point in Deconvolution

Abstract.  We consider estimation of the upper boundary point F ⁻¹ (1) of a distribution function F with finite upper boundary or 'frontier' in deconvolution problems, primarily focusing on deconvolution models where the noise density is decreasing on the positive halfline. Our estimates are based on the (non-parametric) maximum likelihood estimator (MLE) of F . We show that (1) is asymptotically never too small. If the convolution kernel has bounded support the estimator (1) can generally be expected to be consistent. In this case, we establish a relation between the extreme value index of F and the rate of convergence of (1) to the upper support point for the 'boxcar' deconvolution model. If the convolution density has unbounded support, (1) can be expected to overestimate the upper support point. We define consistent estimators , for appropriately chosen vanishing sequences ( β _n ) and study these in a particular case.     

L p –Estimators as Estimates of a Parameter of Location for a Sharp–pointed Symmetric Density

We study the asymptotics of L _p estimators, p > 0, over a sample having a symmetric density with a sharp–point at the centre of symmetry of the distribution. The rates of convergence of the L _p estimators in this situation depend on p and on the shape of the density. To obtain some of the limit distributions, we present new results in the asymptotics of M–estimators. We extend the delta method to the case when the Euclidean norm of the conveniently normalized M–estimators converge to a power of the Euclidean norm of a (possibly Gaussian) stable distribution.