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