Ebook: An Asymptotic Theory for Empirical Reliability and Concentration Processes
- Tags: Statistics general
- Series: Lecture Notes in Statistics 33
- Year: 1986
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-v
Introduction....Pages 1-20
The Basic Setting for the Approximations and Various Preliminaries....Pages 21-33
Auxiliary Processes: Integrals of Empirical Process....Pages 34-38
Mean Residual Life Processes....Pages 39-43
Auxiliary Processes: Empirical Increments of Brownian Bridge Integrals....Pages 44-48
Total Time on Test Processes....Pages 49-60
Scaled Total Time on Test Processes....Pages 61-62
Discussion of Results on Total Time on Test Processes....Pages 63-71
Total Time on Test from the First Failure....Pages 72-80
Unscaled Empirical Lorenz Processes....Pages 81-94
Empirical Lorenz Processes....Pages 95-96
Discussion of Results on Empirical Lorenz Processes....Pages 97-99
The Empirical Concentration Process of Goldie....Pages 100-129
Discussion of Results on the Goldie Concentration Process....Pages 130-134
Further Diversity and Concentration Processes....Pages 135-142
Indices of Inequality, Diversity, and Concentration....Pages 143-149
Bootstrapping Empirical Functions....Pages 150-164
References....Pages 165-171
Back Matter....Pages 172-172
Content:
Front Matter....Pages i-v
Introduction....Pages 1-20
The Basic Setting for the Approximations and Various Preliminaries....Pages 21-33
Auxiliary Processes: Integrals of Empirical Process....Pages 34-38
Mean Residual Life Processes....Pages 39-43
Auxiliary Processes: Empirical Increments of Brownian Bridge Integrals....Pages 44-48
Total Time on Test Processes....Pages 49-60
Scaled Total Time on Test Processes....Pages 61-62
Discussion of Results on Total Time on Test Processes....Pages 63-71
Total Time on Test from the First Failure....Pages 72-80
Unscaled Empirical Lorenz Processes....Pages 81-94
Empirical Lorenz Processes....Pages 95-96
Discussion of Results on Empirical Lorenz Processes....Pages 97-99
The Empirical Concentration Process of Goldie....Pages 100-129
Discussion of Results on the Goldie Concentration Process....Pages 130-134
Further Diversity and Concentration Processes....Pages 135-142
Indices of Inequality, Diversity, and Concentration....Pages 143-149
Bootstrapping Empirical Functions....Pages 150-164
References....Pages 165-171
Back Matter....Pages 172-172
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