Asymptotics of Statistical Estimates Constructedfrom Censored Samples of Distributions with RegularlyVarying Tails
We consider the asymptotic behavior of the Pitman estimators $\hat \theta_n$ for the density location parameter $f(x-\theta)=C(1+\alpha)(x-\theta)^{\alpha}L(x-\theta)$, $x\downarrow \theta $, $\alpha>-1$, $L(x)=1+D_1(1+\ell (1+\alpha)^{-1})x^{\ell }+o(x^{\ell })$, $\ell >0$, by observations ov...
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| Vydáno v: | Theory of probability and its applications Ročník 42; číslo 3; s. 495 - 512 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Philadelphia
Society for Industrial and Applied Mathematics
01.07.1998
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| Témata: | |
| ISSN: | 0040-585X, 1095-7219 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | We consider the asymptotic behavior of the Pitman estimators $\hat \theta_n$ for the density location parameter $f(x-\theta)=C(1+\alpha)(x-\theta)^{\alpha}L(x-\theta)$, $x\downarrow \theta $, $\alpha>-1$, $L(x)=1+D_1(1+\ell (1+\alpha)^{-1})x^{\ell }+o(x^{\ell })$, $\ell >0$, by observations over the first $k$ ordered statistics $(X_n^{(1)},\ldots,X_n^{(k)})$, when $k=k(n)\to \infty$, $k/n\to 0$ as $n\to \infty$. The limiting distributions of $\hat \theta_n$ are described for various values of $\alpha$. Our proofs use properties and asymptotic expansions of the hypergeometric functions in several variables. Simple asymptotically efficient estimators of $\theta$ are given as linear functionals of the ordered statistics. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 |
| ISSN: | 0040-585X 1095-7219 |
| DOI: | 10.1137/S0040585X97976271 |