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December, 1990 Asymptotic Efficient Estimation of the Change Point with Unknown Distributions
Y. Ritov
Ann. Statist. 18(4): 1829-1839 (December, 1990). DOI: 10.1214/aos/1176347881


Suppose $X_1,\cdots, X_n$ are distributed according to a probability measure under which $X_1,\cdots, X_n$ are independent, $X_1 \sim F_0$, for $i = 1,\cdots, \lbrack\theta_n n\rbrack$ and $X_i \sim F^{(n)}$ for $i = \lbrack\theta_nn\rbrack + 1, \cdots, n$ where $\lbrack x\rbrack$ denotes the integer part of $x$. In this paper we consider the asymptotic efficient estimation of $\theta_n$ when the distributions are not known. Our estimator is efficient in the sense that if $F^{(n)} = F_{\eta_n}, \eta_n \rightarrow 0$ and $\{F_\eta\}$ is a regular one-dimensional parametric family of distributions, then the estimator is asymptotically equivalent to the best regular estimator.


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Y. Ritov. "Asymptotic Efficient Estimation of the Change Point with Unknown Distributions." Ann. Statist. 18 (4) 1829 - 1839, December, 1990.


Published: December, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0714.62027
MathSciNet: MR1074438
Digital Object Identifier: 10.1214/aos/1176347881

Primary: 62G05
Secondary: 62G20

Keywords: Asymptotic efficiency , limit of experiments , regular estimator

Rights: Copyright © 1990 Institute of Mathematical Statistics

Vol.18 • No. 4 • December, 1990
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