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Novel Statistical Methods: Quantile ...

Yang, Xin.

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Novel Statistical Methods: Quantile Estimation, Inference, and Related Applications in Medical Research.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Novel Statistical Methods: Quantile Estimation, Inference, and Related Applications in Medical Research./
Author:	Yang, Xin.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
Description:	130 p.
Notes:	Source: Dissertations Abstracts International, Volume: 80-04, Section: B.
Contained By:	Dissertations Abstracts International80-04B.
Subject:	Biostatistics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10930773
ISBN:	9780438456556

Novel Statistical Methods: Quantile Estimation, Inference, and Related Applications in Medical Research.
Yang, Xin.

Novel Statistical Methods: Quantile Estimation, Inference, and Related Applications in Medical Research. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 130 p.

Source: Dissertations Abstracts International, Volume: 80-04, Section: B.

Thesis (Ph.D.)--State University of New York at Buffalo, 2018.

This item must not be added to any third party search indexes.

In this dissertation, selected topics with respect to the quantile estimation, inference, and related applications in medical research are presented. First, new types of quantile estimators are developed. One is based on estimating the moments of fractional order statistics, which quantile density estimators can be derived simultaneously with the quantile estimator. The other is an extension of the well-known Bernstein Polynomial quantile estimator, which can be readily dierentiated to obtain the rst order derivative, i.e. the quantile density estimator. Both methods can deal with censored data in a straightforward and ecient way. Second, we study a general family of distributions, which is generated by providing a base distribution, that is related to the kernel density estimator asymptotically. It includes a reparameterized skew normal distribution and a new class of bimodal distributions as special cases and also hints at a kernel-type density estimator of a single order statistic. Tests of normality are constructed based on this kernel related function, and the kernel-type density estimator is utilized to construct the nonparametric condence interval for an arbitrary quantile based on a Studentized-t analogy that provides a simple and less biased alternative to the traditional bootstrap percentile-t condence interval. Third, we investigate the optimal strategies of estimating the mean and standard deviation. A generalized best linear unbiased estimator (BLUE) is proposed to provide the optimal unbiased estimation for both single studies and the overall study. The approach not only can be easily extended to deal with summary statistics that are not covered in the literature, such as tertiles and deciles, but also makes the global eect and condence interval less likely to be biased as compared with the existing methods.

ISBN: 9780438456556Subjects--Topical Terms:

1002712
Biostatistics.
Subjects--Index Terms:

Bernstein Polynomial quantile estimator

Novel Statistical Methods: Quantile Estimation, Inference, and Related Applications in Medical Research.
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245 1 0 $a Novel Statistical Methods: Quantile Estimation, Inference, and Related Applications in Medical Research.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2018
300 $a 130 p.
500 $a Source: Dissertations Abstracts International, Volume: 80-04, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Hutson, Alan D.
502 $a Thesis (Ph.D.)--State University of New York at Buffalo, 2018.
506 $a This item must not be added to any third party search indexes.
506 $a This item must not be sold to any third party vendors.
520 $a In this dissertation, selected topics with respect to the quantile estimation, inference, and related applications in medical research are presented. First, new types of quantile estimators are developed. One is based on estimating the moments of fractional order statistics, which quantile density estimators can be derived simultaneously with the quantile estimator. The other is an extension of the well-known Bernstein Polynomial quantile estimator, which can be readily dierentiated to obtain the rst order derivative, i.e. the quantile density estimator. Both methods can deal with censored data in a straightforward and ecient way. Second, we study a general family of distributions, which is generated by providing a base distribution, that is related to the kernel density estimator asymptotically. It includes a reparameterized skew normal distribution and a new class of bimodal distributions as special cases and also hints at a kernel-type density estimator of a single order statistic. Tests of normality are constructed based on this kernel related function, and the kernel-type density estimator is utilized to construct the nonparametric condence interval for an arbitrary quantile based on a Studentized-t analogy that provides a simple and less biased alternative to the traditional bootstrap percentile-t condence interval. Third, we investigate the optimal strategies of estimating the mean and standard deviation. A generalized best linear unbiased estimator (BLUE) is proposed to provide the optimal unbiased estimation for both single studies and the overall study. The approach not only can be easily extended to deal with summary statistics that are not covered in the literature, such as tertiles and deciles, but also makes the global eect and condence interval less likely to be biased as compared with the existing methods.
590 $a School code: 0656.
650 4 $a Biostatistics. $3 1002712
650 4 $a Statistics. $3 517247
653 $a Bernstein Polynomial quantile estimator
653 $a fractional order statistics
653 $a kernel density estimator
690 $a 0308
690 $a 0463
710 2 $a State University of New York at Buffalo. $b Biostatistics. $3 2099967
773 0 $t Dissertations Abstracts International $g 80-04B.
790 $a 0656
791 $a Ph.D.
792 $a 2018
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10930773