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oai:www.ideals.illinois.edu:2142/22141 2023-07-10 col_2142_5131 col_2142_17362 com_2142_5130 com_2142_17361 com_2142_8903

Made available in DSpace on 2011-05-07T13:30:18Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9114359.pdf: 2918189 bytes, checksum: a86ffe3dce26cf9fb66ab0d60116692e (MD5) Previous issue date: 1990 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:55:36Z Item is restricted indefinitely. Martinsek, Adam T. Navarro, Mercidita Tulay 2011-05-07T13:30:18Z 2011-05-07T13:30:18Z 10000-01-01 1990 Suppose that $X\sb1,X\sb2,\cdots$ are independent observations from a distribution F, and that one wishes to estimate the $p\sp{\rm th}$ quantile $\xi\sb{p}(0 0).$ If $f(\xi\sb{p})$ is known, one may use the best fixed sample size (i.e., in the sense of minimum risk). If $f(\xi\sb{p})$ is unknown, then the best fixed sample size is also unknown. For this case, a stopping rule T = $T\sb{A}$ is proposed. It is shown that, under certain smoothness conditions on F and a growth condition on the delay, the sequential procedure derived is asymptotically risk efficient, i.e., it performs asymptotically as well as the best fixed-sample-size procedure. In the proof, asymptotic moment bounds for the remainder terms in Bahadur's representations of sample quantiles, and certain central order statistics, are derived and used to verify uniform integrability of $$\left\{\left(A\sp{1/4}\vert \ \xi\sb{pT} - \xi\sb{p}\vert\right)\sp2, A \geq 1\right\}.$$Results are extended to a problem that utilizes a more general loss function, $L\sb{n}\prime = A\vert \ \xi\sb{pn} - \xi\sb{p}\vert\sp{r} + n\ (A > 0, r > 0),$ and to estimation of a linear combination of two quantiles. The problem of estimating the center of a symmetric distribution using the better of the sample mean and the sample median, and that of estimating scale using the better of the sample standard deviation and the sample interquartile range, are studied. Under certain conditions, the risk is minimized (asymptotically) by using the estimator that possesses the smaller asymptotic variance (in scale estimation, the smaller standardized asymptotic variance) and the sample size that minimizes the asymptotic risk of that estimator. Oftentimes, though, the asymptotic variances of the estimators are unknown. In this case, no single estimator and no fixed sample size would minimize the risk. Adaptive sequential procedures that allow one to choose not only the estimators but also the sample sizes in the two problems are investigated. Both interval and point estimation are considered. Restriction data tranferred 2014-07-01T11:25:55-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9114359 (UMI)AAI9114359 http://hdl.handle.net/2142/22141 eng Copyright 1990 Navarro, Mercidita Tulay Statistics Sequential estimation of quantiles and adaptive sequential estimation of location and scale parameters text Statistics Statistics University of Illinois at Urbana-Champaign Dissertation Ph.D.