An Asymptotic Theory for Empirical Reliability and Concentration Processes

1. Front Matter

   Pages i-v

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2. Introduction

   • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

   Pages 1-20

3. The Basic Setting for the Approximations and Various Preliminaries

   • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

   Pages 21-33

4. Auxiliary Processes: Integrals of Empirical Process

   • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

   Pages 34-38

5. Mean Residual Life Processes

   • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

   Pages 39-43

6. Auxiliary Processes: Empirical Increments of Brownian Bridge Integrals

   • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

   Pages 44-48

7. Total Time on Test Processes

   • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

   Pages 49-60

8. Scaled Total Time on Test Processes

   • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

   Pages 61-62

9. Discussion of Results on Total Time on Test Processes

   • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

   Pages 63-71

10. Total Time on Test from the First Failure

    • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

    Pages 72-80

11. Unscaled Empirical Lorenz Processes

    • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

    Pages 81-94

12. Empirical Lorenz Processes

    • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

    Pages 95-96

13. Discussion of Results on Empirical Lorenz Processes

    • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

    Pages 97-99

14. The Empirical Concentration Process of Goldie

    • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

    Pages 100-129

15. Discussion of Results on the Goldie Concentration Process

    • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

    Pages 130-134

16. Further Diversity and Concentration Processes

    • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

    Pages 135-142

17. Indices of Inequality, Diversity, and Concentration

    • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

    Pages 143-149

18. Bootstrapping Empirical Functions

    • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

    Pages 150-164

19. References

    • Miklós Csörgő, Sándor Csörgő, Lajos Horváth

    Pages 165-171

20. Back Matter

    Pages 172-172

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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.

• Bootstrapping
• Variance
• probability
• statistics

• Department of Mathematics and Statistics, Carleton University, Ottawa, Canada

  Miklós Csörgő

• Bolyai Institute, Szeged University, Szeged, Hungary

  Sándor Csörgő, Lajos Horváth

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