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Statistical Inference on Residual Life

Part of the Statistics for Biology and Health Book Series

DOI: 10.1007/978-1-4939-0005-3

ISBN: 978-1-4939-0004-6

Publisher: Springer New York - Springer Journals

Dec 14, 2013

Available

Introduction

Jeong, Jong-Hyeon

Pages: 1 –18

[In this chapter, we review some fundamental mathematical tools often used in development of probability and statistics theory, especially for the quantile (residual life) function, such as almost sure convergence, strong law of large numbers (SLLN), empirical processes, quantile processes,...
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Inference on Mean Residual Life-Overview

Jeong, Jong-Hyeon

Pages: 19 –26

[Statistical inference based on the remaining lifetimes would be intuitively more appealing than the popular hazard function defined as the risk of immediate failure, whose interpretation could be sometimes difficult to be grasped. For example, when an efficacy of a new drug is concerned, it...
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Quantile Residual Life

Jeong, Jong-Hyeon

Pages: 27 –76

[As mentioned in Chapter 2, the mean residual life function is sensitive to outliers. In this chapter, as an alternative we consider the quantile residual life function, which is robust under any skewed distribution. We first review asymptotic theories of the quantile function and quantile...
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Quantile Residual Life Under Competing Risks

Jeong, Jong-Hyeon

Pages: 77 –117

[Competing risks data are often encountered in many research areas such as medicine, engineering, and econometrics whenever one type of events precludes other types of events from being observed. For example, in cancer research, investigators might want to know a drug effect that would only...
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Other Methods for Inference on Quantiles

Jeong, Jong-Hyeon

Pages: 119 –139

[While the quantiles have many advantages including robustness, straightforward interpretation, and presentation of specific information, they also suffer from some pitfalls. First of all, evaluation of the variance formulas of the quantiles involves estimation of the probability density function...
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Study Design Based on Quantile (Residual Life)

Jeong, Jong-Hyeon

Pages: 141 –149

[Statistical design of a time-to-event study is usually based on the log-rank test, which is optimal for the proportional hazards model to test for the hazard ratio. However, it would be more straightforward to design a study to test for a difference in quantile (residual) lifetimes, say to...

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