Journal ArticleDOI
Testing for uniform stochastic ordering via empirical likelihood
Hammou El Barmi,Ian W. McKeague +1 more
TLDR
In this article, an empirical likelihood approach to testing for the presence of uniform stochastic ordering (or hazard rate ordering) among univariate distributions based on independent random samples from each distribution is developed.Abstract:
This paper develops an empirical likelihood approach to testing for the presence of uniform stochastic ordering (or hazard rate ordering) among univariate distributions based on independent random samples from each distribution. The proposed test statistic is formed by integrating a localized empirical likelihood statistic with respect to the empirical distribution of the pooled sample. The asymptotic null distribution of this test statistic is found to have a simple distribution-free representation in terms of standard Brownian motion. The approach is extended to the case of right-censored survival data via multiple imputation. Two applications are discussed: (1) uncensored survival time data of mice exposed to radiation, and (2) right-censored time-to-infection data from a human HIV vaccine trial comparing a placebo group with a vaccine group.read more
Citations
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Book ChapterDOI
Convergence of probability measures
TL;DR: Weakconvergence methods in metric spaces were studied in this article, with applications sufficient to show their power and utility, and the results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables.
Journal Article
Approximating the likelihood in approximate Bayesian computation
TL;DR: In this article, the authors present two alternative approaches for estimating the intractable likelihood, with the goal of reducing the necessary model simulations to produce an approximate posterior, which can be used to completely avoid model simulations in some cases.
Journal ArticleDOI
Testing for positive quadrant dependence.
TL;DR: Simulation results show the EL testing procedure performs well in a variety of scenarios when X and Y are strictly PQD, and a distribution-free test statistic is created that integrates a localized EL ratio test statistic with respect to the empirical joint distribution ofX and Y.
Journal ArticleDOI
Testing for uniform stochastic orderings via empirical likelihood under right censoring
TL;DR: In this article, empirical likelihood based tests for the presence of uniform stochastic ordering (or hazard rate ordering) among two univariate distributions functions (DFs) are developed when the data are right censored in the one and two-sample cases.
Journal ArticleDOI
Restricted estimation of the cumulative incidence functions of two competing risks
TL;DR: In this article, the authors consider the estimation of two cumulative incidence functions, F 1 and F 2, corresponding to two competing risks when the ratio R ( t ) ≡ F 1 (t ) / F 2 (t) is nondecreasing in t > 0.
References
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Book ChapterDOI
Nonparametric Estimation from Incomplete Observations
Edward L. Kaplan,Paul Meier +1 more
TL;DR: In this article, the product-limit (PL) estimator was proposed to estimate the proportion of items in the population whose lifetimes would exceed t (in the absence of such losses), without making any assumption about the form of the function P(t).
Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Book
Weak Convergence and Empirical Processes: With Applications to Statistics
TL;DR: In this article, the authors define the Ball Sigma-Field and Measurability of Suprema and show that it is possible to achieve convergence almost surely and in probability.
BookDOI
Weak Convergence and Empirical Processes
TL;DR: This chapter discusses Convergence: Weak, Almost Uniform, and in Probability, which focuses on the part of Convergence of the Donsker Property which is concerned with Uniformity and Metrization.
Journal ArticleDOI
The Statistical Analysis of Failure Time Data
TL;DR: This book complements the other references well, and merits a place on the bookshelf of anyone concerned with the analysis of lifetime data from any eld.
Related Papers (5)
Empirical likelihood based tests for stochastic ordering under right censorship.
Hsin-wen Chang,Ian W. McKeague +1 more