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作者：FAN, JQ; HALL, P
作者单位：Australian National University
摘要：The local median regression method has long been known as a robustified alternative to methods such as local mean regression. Yet, its optimal statistical properties are largely unknown. In this paper, we show via decision-theoretic arguments that a local weighted median estimator is the best least absolute deviation estimator in an asymptotic minimax sense, under L(1)-loss. We also study asymptotic efficiency of the local median estimator in the class of all possible estimators. From a practi...
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作者：HARTIGAN, JA
摘要：Observations X(i) are uncorrelated with means theta(i), i = 1,...,n, and variances 1. The linear estimators theta = TX, for some n x n matrix T, are widely used in smoothing problems, where it is assumed that neighbouring parameter Values are similar The smoothness assumption is violated in change point problems, where neighbouring parameter values are equal, except at some unspecified change points where there are jumps of unknown size from one parameter value to the next. In the case of a si...
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作者：KASS, RE; SLATE, EH
作者单位：Cornell University
摘要：Standard large-sample maximum likelihood and Bayesian inference, based on limiting multivariate normal distributions, may be dubious when applied with small or moderate sample sizes. We define and discuss several measures of nonnormality of MLE and posterior distributions that may be used as diagnostics and can indicate whether reparameterization will be effective in improving inferences. We begin by showing how the nonlinearity measures introduced by Beale and Bates and Watts for nonlinear re...
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作者：XIANG, XJ
作者单位：University of Chicago
摘要：In this paper, two versions of the Berry-Esseen theorems are established for L-statistics in the non-identically distributed case. One theorem, which requires E\X(i)\(3) < infinity, is an extension of the classical Berry-Esseen theorem. Another, proved under the condition E\X(i)\(alpha) < infinity for some alpha is an element of (0, 1], seems to be of more interest for statistical inference. Some applications are also discussed.
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作者：MURPHY, SA
摘要：The frailty model is a generalization of Cox's proportional hazards model which includes a random effect. Nielsen, Gill, Andersen and Sorensen proposed an EM algorithm to estimate the cumulative baseline hazard and the variance of the random effect. Here existence and consistency of the estimators are proved. An example using truncated and censored data is considered.
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作者：DEVROYE, L
摘要：We use the probabilistic method to show that iff(nh) is the standard kernel estimate with smoothing factor h, then there exists a deterministic sequence h(n) such that, for all densities, [GRAPHICS]
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作者：SHAO, J
摘要：We study linear combinations of order statistics (L-statistics) in survey problems with a stratified multistage sampling design. Two general types of L-statistics are considered: smooth L-statistics with weights generated by a smooth function and nonsmooth L-statistics (sample quantiles). The trimmed sample mean, the decile mean and variance, the sample Lorenz curve and the sample Gini's family parameters are examples of smooth L-statistics or functions of smooth L-statistics used in survey pr...
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作者：FYGENSON, M; RITOV, Y
作者单位：Hebrew University of Jerusalem
摘要：The monotone class rank-test-based estimating equations for regression models with right censored data is considered. We introduce an estimator which is a solution of a monotone estimating equation that is an extension of the Gehan test. The estimator is easy to derive, root n-consistent and asymptotically normal under minimal conditions. All monotone estimating equations are characterized, and a simulation study, which shows that our suggested procedure performs well, is included.
