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Teoriya Veroyatnostei i ee Primeneniya, 1976, Volume 21, Issue 1, Pages 16–33
(Mi tvp3272)
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This article is cited in 17 scientific papers (total in 17 papers)
Asymptotic expansions associated with some statistical estimates in the smooth case. II. Expansions of moments and distributions
S. I. Gusev Leningrad
Abstract:
Let $x_1,\dots,x_n$ be a sample from a distribution $\mathbf P_{\theta}$ with density $f(x,\theta)$, $\theta\in \Theta\subset R^1$. Let $T_n$ be a Bayesian estimate or a maximum posterior density estimate. The expansions
$$
\sqrt n(T_n-\theta)=\xi_0+\xi_1\frac{1}{\sqrt n}+\dots+\xi_{k-1}\biggl(\frac{1}{\sqrt n}\biggr)^{k-1}+\widetilde\xi_{k,n}\biggl(\frac{1}{\sqrt n}\biggr)^k,
$$
obtained in [1], imply expansions of the moments $\mathbf E_{\theta}(\sqrt n(T_n-\theta))^m$ where $m\ge 1$ is an integer, and expansions of the distribution functions $\mathbf P_{\theta}\{\sqrt n(T_n-\theta)<z\}$. Linnik's problem of calculating the terms of order $1/n$ in the expansion of $\mathbf E_{\theta}(\sqrt n(T_n-\theta))^2$ is solved.
Received: 11.03.1975
Citation:
S. I. Gusev, “Asymptotic expansions associated with some statistical estimates in the smooth case. II. Expansions of moments and distributions”, Teor. Veroyatnost. i Primenen., 21:1 (1976), 16–33; Theory Probab. Appl., 21:1 (1976), 14–33
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https://www.mathnet.ru/eng/tvp3272 https://www.mathnet.ru/eng/tvp/v21/i1/p16
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Abstract page: | 171 | Full-text PDF : | 71 |
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