The rates of convergence of Bayes estimators in change-point analysis

Statistics and Probability Letters

Volumn 27, Issue 4, 1996, Pages 319-329

  Rukhin, Andrew L ^a  

^a UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

Author keywords

Bayes risk; Change point problem; Convergence rate; Geometric distribution; Maximum likelihood estimator; Spitzer's formula; Zero one loss function

Indexed keywords

EID: 0030136564     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-7152(95)00093-3     Document Type: Article

References (14)

1. Brodsky, B.E. and B.S. Darkhovsky (1993), Nonparametric Methods in Change-Point Problems (Kluwer, Dordrecht).
2. Chernoff, H. (1972), Sequential Analysis and Optimal Design, Regional Conferences Series in Applied Mathematics (SIAM, Philadelphia, PA).
3. Dümbgen, L. (1991), The asymptotic behavior of some nonparametric change-point estimators. Ann. Statist. 19, 1471-1495.
4. Ferger, D. and W. Stute (1992), Convergence of changepoint estimators, Stochastic Proc. Appl. 42, 345-351.
5. Hinkley, D.V. (1970), Inference about the change-point in a sequence of random variables, Biometrika 57, 1-17.
6. Plachky, D. and A.L. Rukhin (1994), Unbiasedness and sufficiency in the change-point problem, in: P. Lachout and J.A. Visek, ed., Proc. 12th Prague Conf. on Information Theory, Statistical Decision Functions and Random Processes (Academy of Sciences of Czech Republic, Prague).
7. Robbins, H. (1954), A remark on the joint distribution of cumulative sums, Ann. Math. Statist. 25, 614-616.
8. Rukhin, A.L. (1994), Asymptotic minimaxity in the change-point problem, in: D. Siegmund, E. Carlstein and H. Mueller, eds., Proc. on Change-Point Problems (Institute of Mathematical Statistics, Hayward, CA).
9. Rukhin, A.L. (1996), Change-point estimation: linear statistics, Bayes risk and an information distance, Math. Methods Statist. 5.
10. Spitzer, F. (1996), Principles of Random Walk (Van Nostrand, New York).
11. Stone, C.J. (1965), On moment generating function and renewal theory, Ann. Math. Statist. 36, 1298-1301.
12. Woodroofe, M. (1982), Nonlinear Renewal Theory in Sequential Analysis, Regional Conferences Series in Applied Mathematics (SIAM, Philadelphia, PA).
13. Yao, Y., D. Huang and R.A. Davis (1994), On almost sure behavior of change-point estimators, In: D. Siegmund, E. Carlstein and H. Mueller, eds., Proc. on Change-Point Problems (Institute of Mathematical Statistics, Hayward, CA).
14. Yao, Y.C. (1987), Approximating the distribution of the maximum likelihood estimate of the change-point in a sequence of independent random variables, Ann. Statist. 15, 1321-1328.