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Nonparametric Density and Hazard Rate Estimation for Missing Right Censored Data /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Nonparametric Density and Hazard Rate Estimation for Missing Right Censored Data /Lirit Fuksman.
Author:	Fuksman, Lirit,
Description:	1 electronic resource (211 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 87-06, Section: B.
Notes:	Advisors: Efromovich, Sam; Smaldone, Ronald Committee members: Li, Qiwei; Choudhary, Pankaj; Chiou, Sy Han.
Contained By:	Dissertations Abstracts International87-06B.
Subject:	Statistics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32435788
ISBN:	9798265467355

Nonparametric Density and Hazard Rate Estimation for Missing Right Censored Data /
Fuksman, Lirit,

Nonparametric Density and Hazard Rate Estimation for Missing Right Censored Data /Lirit Fuksman. - 1 electronic resource (211 pages)

Source: Dissertations Abstracts International, Volume: 87-06, Section: B.

Orthogonal series estimation is a powerful nonparametric technique for estimating curves without making any shape or distributional assumptions. The statistical problem considered is the nonparametric estimation of density and hazard rate functions based on data modified by missing and right censoring. Marginal and conditional densities, as well as hazard rates, are studied, and a glimpse of bivariate density estimation is provided as an extension. For missing completely at random (MCAR) and missing at random (MAR) mechanisms, the asymptotic theory of sharp minimax estimation is developed, demonstrating that the data modifications do not affect the rate of convergence under the mean integrated squared error criterion, but they do increase the constant of convergence. An interesting conclusion drawn from the theory is that the rougher the density, the less sensitive density estimation is to the missingness. The theory is complemented by proposing an algorithm for a data-driven estimator for small samples which is tested on numerical simulations and real data. Moreover, common imputation procedures are compared with the proposed estimator, and it is argued that the proposed estimator often outperforms the imputation methods.

English

ISBN: 9798265467355Subjects--Topical Terms:

182057
Statistics.
Subjects--Index Terms:

Missing completely at random

Nonparametric Density and Hazard Rate Estimation for Missing Right Censored Data /
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500 $a Advisors: Efromovich, Sam; Smaldone, Ronald Committee members: Li, Qiwei; Choudhary, Pankaj; Chiou, Sy Han.
502 $b Ph.D. $c The University of Texas at Dallas $d 2025.
520 $a Orthogonal series estimation is a powerful nonparametric technique for estimating curves without making any shape or distributional assumptions. The statistical problem considered is the nonparametric estimation of density and hazard rate functions based on data modified by missing and right censoring. Marginal and conditional densities, as well as hazard rates, are studied, and a glimpse of bivariate density estimation is provided as an extension. For missing completely at random (MCAR) and missing at random (MAR) mechanisms, the asymptotic theory of sharp minimax estimation is developed, demonstrating that the data modifications do not affect the rate of convergence under the mean integrated squared error criterion, but they do increase the constant of convergence. An interesting conclusion drawn from the theory is that the rougher the density, the less sensitive density estimation is to the missingness. The theory is complemented by proposing an algorithm for a data-driven estimator for small samples which is tested on numerical simulations and real data. Moreover, common imputation procedures are compared with the proposed estimator, and it is argued that the proposed estimator often outperforms the imputation methods.
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650 4 $a Biostatistics. $3 339693
653 $a Missing completely at random
653 $a Missing at random
653 $a Nonparametric density
653 $a Nonparametric curve estimation
653 $a Hazard rate
653 $a Density estimation
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710 2 $a The University of Texas at Dallas. $b Statistics. $e degree granting institution. $3 1010523
720 1 $a Efromovich, Sam $e degree supervisor.
720 1 $a Smaldone, Ronald $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 87-06B.
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791 $a Ph.D.
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