Asymptotically optimal estimation of smooth functionals for interval censoring, part 2

Estimation in the interval censoring model is considered. A class of smooth functionals is introduced, of which the mean is an example. We consider case 2, with two observation times for each unobservable event time, in the situation that the observation times cannot become arbitrarily close to each other. It is proved that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound.     

基于定数截尾样本的指数分布的环境因子估计

讨论了定数截尾样本下,指数分布环境因子的极大似然估计和区间估计,为研究估计的精度,运用随机模拟方法,对环境因子的置信区间的精度进行了讨论。     

Nonparametric estimators of the bivariate survival function under random censoring

A large number of proposals for estimating the bivariate survival function under random censoring have been made. In this paper we discuss the most prominent estimators, where prominent is meant in the sense that they are best for practical use; Dabrowska's estimator, the Prentice–Cai estimator, Pruitt's modified EM-estimator, and the reduced data NPMLE of van der Laan. We show how these estimators are computed and present their intuitive background. The asymptotic results are summarized. Furthermore, we give a summary of the practical performance of the estimators under different levels of dependence and censoring based on extensive simulation results. This leads also to a practical advise.     

MULTIPLE FAILURE CAUSES AND OBSERVATIONS OF TIME DEPENDENT COVARIABLES

In this paper firstly a summary of the theory of competing risks is presented; it shows how cause specific failure time distributions, failure probabilities and failure rate functions relate to the joint survivor function in the presence of various competing failure causes. This first part of the paper gives the insight useful for the second part, which concerns the way in which the dependency of the failure process on given time–dependent observations of covariables is specified and estimated. An application is presented briefly.     

Maximum likelihood methods for fitting the burr type XII distribution to multiply (progressively) censored life test data

Summary This paper develops mathematical and computational methodology for fitting, by the method of maximum likelihood (ML), the Burr Type XII distribution to multiply (or progressively) censored life test data. Mathematical expressions are given for approximating the asymptotic variances and covariances of the ML estimates (MLEs) of the parameters of the Burr Type XII distribution. A rigorous mathematical analysis is undertaken to investigate the existence and uniqueness of the MLEs for arbitrary sample data. The methodology of this paper is applied to progressively censored sample data arising in a life test experiment.     

Efficiency Considerations in the Additive Hazards Model with Current Status Data

For current status data, L IN , O AKES and Y ing (1998) proposed a procedure for estimation of the regression parameters in the additive hazards model that makes clever use of martingale theory. However, one of the outstanding problems posed in the paper was the issue of efficient estimation, as their estimators do not attain the semiparametric information bound. In this paper, we explore this issue and provide a characterization of the NPMLE. We conduct efficiency comparisons between the NPMLE and the procedure of L IN et al . (1998) analytically and numerically through analysis of a dataset from a tumorigenicity experiment.     

Constructive identification of the mixed proportional hazards model

We give a new proof of the identifiably of the MPH model. This proof is constructive: it is a recipe for constructing the triple—regression function, base-line hazard, and distribution of the individual effect—from the observed cumulative distribution functions.
We then prove that the triples do not depend continuously on the observed cumulative distribution functions. Uniformly consistent estimators do not exist.
Finally we show that the MPH model is even identifiable from two-sided censored observations. This proof is constructive, too.     

Asymptotic normality of the NPMLE of linear functionals for interval censored data, case 1

We give a new proof of the asymptotic normality of a class of linear functionals of the nonparametric maximum likelihood estimator (NPMLE) of a distribution function with "case 1" interval censored data. In particular our proof simplifies the proof of asymptotic normality of the mean given in Groeneboom and Wellner (1992). The proof relies strongly on a rate of convergence result due to van de Geer (1993), and methods from empirical process theory.     

Maximum Likelihood Estimation of a General Unbalanced Spatial Random Effects Model: a Monte Carlo Study

Abstract

This paper discusses the maximum likelihood estimator of a general unbalanced spatial random effects model with normal disturbances, assuming that some observations are missing at random. Monte Carlo simulations show that the maximum likelihood estimator for unbalanced panels performs well and that missing observations affect mainly the root mean square error. As expected, these estimates are less efficient than those based on the unobserved balanced model, especially if the share of missing observations is large or spatial autocorrelation in the error terms is pronounced.

Estimation de vraisemblance maximale d'un modèle général d'effets aléatoires spatiaux déséquilibré: une étude Monte Carlo

RÉSUMÉ La présente communication se penche sur l'estimateur du maximum de vraisemblance d'un modèle général d'effets aléatoires spatiaux déséquilibré avec des perturbations normales, en supposant l'absence aléatoire de certaines observations. Des simulations de Monte Carlo montrent que des groupes déséquilibrés se comporte bien, et que les observations manquantes affectent principalement l'erreur de la moyenne quadratique. Comme prévu, ces évaluations sont moins efficaces que celles qui sont basées sur le modèle équilibré non observé, notamment si la part des observations manquantes est importantes, ou l'on déclare une autocorrélation spatiale dans les termes d'erreur.

Estimación de la probabilidad máxima de un modelo espacial general desequilibrado de efectos al azar: un estudio de Monte Carlo

RÉSUMÉN Este trabajo discute el estimador de probabilidad máxima de un modelo espacial general desequilibrado de efectos al azar con alteraciones normales, suponiendo que faltan algunas observaciones al azar. Las simulaciones de Monte Carlo muestran que el estimador de probabilidad máxima para los paneles desequilibrados funciona satisfactoriamente, y que las observaciones omisas afectan principalmente al error de la media cuadrática. Como se suponía, estas estimaciones son menos eficientes que las basadas en el modelo equilibrado inadvertido, especialmente si la cantidad de omisiones es grande/o la autocorrelación en los términos de error es pronunciada.

     

Conditional inference procedures for the Laplace distribution when the observed samples are progressively censored

In this paper, we develop procedures for obtaining confidence intervals for the parameters of a Laplace distribution as well as upper and lower γ probability tolerance intervals for a proportion β, given a progressively Type-II right censored sample from the Laplace distribution. The intervals are obtained by conditioning on the observed values of the ancillary statistics. The intervals are exact, do not require numerical integration, and generalize the work of Childs and Balakrishnan (1996) who considered the conventional Type-II right censored case. Received: February 2000     

Estimating the Derivative of a Convex Density

We obtain a relation between the time between two bird-catchings and the total resting period of a bird, leading to the problem of estimating the derivative of a convex density. We state a fundamental result on the nonparametric maximum likelihood estimator of a convex density. Further, we derive the optimal rate in the minimax risk sense for estimating the derivative of a convex density.