Consistency of the generalized MLE of a joint distribution function with multivariate interval-censored data

AbstractWong and Yu [Generalized MLE of a joint distribution function with multivariate interval-censored data, J. Multivariate Anal. 69 (1999) 155–166] discussed generalized maximum likelihood estimation of the joint distribution function of a multivariate random vector whose coordinates are subject to interval censoring. They established uniform consistency of the generalized MLE (GMLE) of the distribution function under the assumption that the random vector is independent of the censoring vector and that both of the vector distributions are discrete. We relax these assumptions and establish consistency results of the GMLE under a multivariate mixed case interval censorship model. van der Vaart and Wellner [Preservation theorems for Glivenko–Cantelli and uniform Glivenko–Cantelli class, in: E. Gine, D.M. Mason, J.A. Wellner (Eds.), High Dimensional Probability, vol. II, Birkhäuser, Boston, 2000, pp. 115–133] and Yu [Consistency of the generalized MLE with multivariate mixed case interval-censored data, Ph.D Dissertation, Binghamton University, 2000] independently proved strong consistency of the GMLE in the L1(μ)-topology, where μ is a measure derived from the joint distribution of the censoring variables. We establish strong consistency of the GMLE in the topologies of weak convergence and pointwise convergence, and eventually uniform convergence under appropriate distributional assumptions and regularity conditions

ASYMPTOTIC DISTRIBUTIONS OF THE BUCKLEY-JAMES ESTIMATOR UNDER NONSTANDARD CONDITIONS

Abstract: The Buckley-James estimator (BJE) is the most appropriate extension of the least squares estimator (LSE) to the right-censored linear regression model

ASYMPTOTIC PROPERTIES OF THE GENERALIZED SEMI-PARAMETRIC MLE IN LINEAR REGRESSION

Abstract: Consider the semi-parametric linear regression model, Y = β X + , with sample size n, where has an unknown cdf Fo. The semi-parametric MLE (SMLE) βn of β under this set-up, called the generalized SMLE or GSMLE, has neither been studied in the literature nor an algorithm for it. We begin with an algorithm for the GSMLE. It is then shown that if Fo has a discontinuity point, P{βn = β if n is large} = 1. Simulation suggests that under some discontinuous distributions, βn = β even for n = 50. In contrast the least squares estimator (LSE),βn, satisfies P{βn = β i.o.} = 1. We demonstrate via a real discontinuous data example that the GSMLE can be better than the LSE in applications. Properties of the GSMLE in the continuous case are also mentioned

Functional variant of the carboxypeptidase M (CPM) gene may affect silica-related pneumoconiosis susceptibility by its expression: a multistage case-control study.

ObjectivesIn a genome-wide association study, we discovered chromosome 12q15 (defined as rs73329476) as a silica-related pneumoconiosis susceptibility region. However, the causal variants in this region have not yet been reported.MethodsWe systematically screened eight potentially functional single-neucleotide polymorphism (SNPs) in the genes near rs73329476 (carboxypeptidase M (CPM) and cleavage and polyadenylation specific factor 6 (CPSF6)) in a case-control study including 177 cases with silicosis and 204 healthy controls, matched to cases with years of silica dust exposure. We evaluated the associations between these eight SNPs and the development of silicosis. Luciferase reporter gene assays were performed to test the effects of selected SNP on the activity of CPM in the promoter. In addition, a two-stage case-control study was performed to investigate the expression differences of the two genes in peripheral blood leucocytes from a total of 64 cases with silicosis and 64 healthy controls with similar years of silica dust exposure as the cases.ResultsWe found a strong association between the mutant rs12812500 G allele and the susceptibility of silicosis (OR=1.45, 95% CI 1.03 to 2.04, p=0.034), while luciferase reporter gene assays indicated that the mutant G allele of rs12812500 is strongly associated with increased luciferase levels compared with the wild-type C allele (p<0.01). Moreover, the mRNA (peripheral blood leucocytes) expression of the CPM gene was significantly higher in subjects with silicosis compared with healthy controls.ConclusionsThe rs12812500 variant of the CPM gene may increase silicosis susceptibility by affecting the expression of CPM, which may contribute to silicosis susceptibility with biological plausibility

Admissibility of the Empirical Distribution Function in discrete nonparametric invariant problems

Consider nonparametric problems of estimating an unknown distribution function, F, under the loss L(F,a)=[integral operator] F(t)-a(t)2(F(t))[alpha](1 -F(t))[beta]dF(t), where [alpha][set membership, variant][-1,0] and [beta][set membership, variant][-1,1]. It is proved that the Empirical Distribution Function (EDF) is admissible (extending a result of Brown, 1988). Among them, an important case is the loss L(F,a)=[integral operator]F(t)- a(t)2dF(t).Admissibility invariant estimator nonparametric estimator discrete distribution stepwise Bayes procedure

A note on the proportional hazards model with discontinuous data

Cox's proportional hazards (PH) model is applicable to continuous random (response) variables as well as to discontinuous ones. We make two remarks on the PH models for discontinuous random (response) variables. (1) In general, the proportional hazards relation can only occur in the interior of the support of the two relevant random variables, instead on the whole support, as stated in the standard textbooks. (2) The PH model is not the same as a proportional cumulative hazards model (or a Lehmann family) unless the random variables are continuous. These two models are mistaken to be the same in several papers on Cox's regression model in the literature.Survival data Cumulative hazards Regression models Discrete distributions Lehmann family

Admissibility of linear estimators in the fisheries census

admissibility, discrete parameter estimation, linear estimator,