BOOTSTRAP AND RELATED METHODS FOR APPROXIMATE CONFIDENCE BOUNDS IN NONPARAMETRIC REGRESSION.

Persistent Link:
http://hdl.handle.net/10150/183923
Title:
BOOTSTRAP AND RELATED METHODS FOR APPROXIMATE CONFIDENCE BOUNDS IN NONPARAMETRIC REGRESSION.
Author:
RUTHERFORD, BRIAN MILNE.
Issue Date:
1986
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The problem considered relates to estimating an arbitrary regression function m(x) from sample pairs (Xᵢ,Yᵢ) 1 ≤ i ≤ n. A model is assumed of the form Y = m(x) + ε(x) where ε(x) is a random variable with expectation 0. One well known method for estimating m(x) is by using one of a class of kernel regression estimators say m(n)(x). Schuster (1972) has shown conditions under which the limiting distribution of the kernel estimator m(n)(x) is the normal distribution. It might also be of interest to use the data to estimate the distribution of m(n)(x). One could, given this estimate, construct approximate confidence bounds for the function m(x). Three estimators are proposed for the density of m(n)(x). They share a basis in non-parametric kernel regression and utilize bootstrap techniques to obtain the density estimate. The order of convergence of one of the estimators is examined and conditions are given under which the order is higher then when estimation is by the normal approximation. Finally the performance of each estimator for constructing confidence bounds is compared for moderate sample sizes using computer studies.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Regression analysis.; Nonparametric statistics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Systems and Industrial Engineering; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Yakowitz, Sidney

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleBOOTSTRAP AND RELATED METHODS FOR APPROXIMATE CONFIDENCE BOUNDS IN NONPARAMETRIC REGRESSION.en_US
dc.creatorRUTHERFORD, BRIAN MILNE.en_US
dc.contributor.authorRUTHERFORD, BRIAN MILNE.en_US
dc.date.issued1986en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe problem considered relates to estimating an arbitrary regression function m(x) from sample pairs (Xᵢ,Yᵢ) 1 ≤ i ≤ n. A model is assumed of the form Y = m(x) + ε(x) where ε(x) is a random variable with expectation 0. One well known method for estimating m(x) is by using one of a class of kernel regression estimators say m(n)(x). Schuster (1972) has shown conditions under which the limiting distribution of the kernel estimator m(n)(x) is the normal distribution. It might also be of interest to use the data to estimate the distribution of m(n)(x). One could, given this estimate, construct approximate confidence bounds for the function m(x). Three estimators are proposed for the density of m(n)(x). They share a basis in non-parametric kernel regression and utilize bootstrap techniques to obtain the density estimate. The order of convergence of one of the estimators is examined and conditions are given under which the order is higher then when estimation is by the normal approximation. Finally the performance of each estimator for constructing confidence bounds is compared for moderate sample sizes using computer studies.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectRegression analysis.en_US
dc.subjectNonparametric statistics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineSystems and Industrial Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorYakowitz, Sidneyen_US
dc.identifier.proquest8702351en_US
dc.identifier.oclc697840213en_US
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