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June, 1977 Weak Convergence of the Rao-Blackwell Estimator of a Distribution Function
B. B. Bhattacharyya, P. K. Sen
Ann. Probab. 5(3): 500-510 (June, 1977). DOI: 10.1214/aop/1176995813


Under the condition that the minimal sufficient statistics are transitive, the sequence of Rao-Blackwell estimators of distribution function has been shown to form a reverse martingale sequence. Weak convergence of the corresponding empirical process to a Gaussian process has been established by assuming that the sufficient statistics are $U$-statistics and utilizing certain results on the convergence of conditional expectations of functions of $U$-statistics along with the functional central limit theorems for (reverse) martingales by Loynes (1970) and Brown (1971).


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B. B. Bhattacharyya. P. K. Sen. "Weak Convergence of the Rao-Blackwell Estimator of a Distribution Function." Ann. Probab. 5 (3) 500 - 510, June, 1977.


Published: June, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0362.60020
MathSciNet: MR443018
Digital Object Identifier: 10.1214/aop/1176995813

Primary: 60B10
Secondary: 62B99

Keywords: $U$-statistics , Gaussian process , Rao-Blackwell estimator , reverse martingale , transitive sufficiency , weak convergence

Rights: Copyright © 1977 Institute of Mathematical Statistics


Vol.5 • No. 3 • June, 1977
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