An Asymptotic Theory for Empirical Reliability and Concentration Processes

by Miklos Csïrgï, Sandor Csïrgï, Lajos Horvïth

Overview

Mik16s Cs6rgO and David M. Mason initiated their collaboration on the topics of this book while attending the CBMS-NSF Regional Confer­ ence at Texas A & M University in 1981. Independently of them, Sandor Cs6rgO and Lajos Horv~th have begun their work on this subject at Szeged University. The idea of writing a monograph together was born when the four of us met in the Conference on Limit Theorems in Probability and Statistics, Veszpr~m 1982. This collaboration resulted in No. 2 of Technical Report Series of the Laboratory for Research in Statistics and Probability of Carleton University and University of Ottawa, 1983. Afterwards David M. Mason has decided to withdraw from this project. The authors wish to thank him for his contributions. In particular, he has called our attention to the reverse martingale property of the empirical process together with the associated Birnbaum-Marshall inequality (cf.,the proofs of Lemmas 2.4 and 3.2) and to the Hardy inequality (cf. the proof of part (iv) of Theorem 4.1). These and several other related remarks helped us push down the 2 moment condition to EX < 00 in all our weak approximation theorems.

Product Details

ISBN-13:	9780387963594
Publisher:	Springer New York
Publication date:	07/17/1998
Series:	Lecture Notes in Statistics , #33
Edition description:	1986
Pages:	173
Product dimensions:	0.00(w) x 0.00(h) x 0.02(d)

Table of Contents

l. Introduction.- 2. The basic setting for the approximations and variance preliminaries.- 3. Auxiliary processes: Integrals of empirical processes.- 4. Mean residual life processes.- 5. Auxiliary processes: Empirical increments of Brownian bridge integrals.- 6. Total time on test processes.- 7. Scaled total time on test processes.- 8. Discussion of results on total time on test processes.- 9. Total time on test from the first failure.- 10. Unscaled empirical Lorenz processes.- 11. Empirical Lorenz processes.- 12. Discussion of results on empirical Lorenz processes.- 13. The empirical concentration process of Goldie.- 14. Discussion of results on the Goldie concentration process.- 15. Further diversity and concentration processes.- 16. Indices of inequality, diversity, and concentration.- 17. Bootstrapping empirical functionals.- 18. References.