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Statistical properties of Gaussian r...

Dong, Hua.

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Statistical properties of Gaussian reproducing kernel in density estimation.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Statistical properties of Gaussian reproducing kernel in density estimation./
Author:	Dong, Hua.
Description:	74 p.
Notes:	Source: Dissertation Abstracts International, Volume: 69-09, Section: B, page: 5506.
Contained By:	Dissertation Abstracts International69-09B.
Subject:	Applied Mechanics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3325302
ISBN:	9780549790617

Statistical properties of Gaussian reproducing kernel in density estimation.
Dong, Hua.

Statistical properties of Gaussian reproducing kernel in density estimation. - 74 p.

Source: Dissertation Abstracts International, Volume: 69-09, Section: B, page: 5506.

Thesis (Ph.D.)--University of Minnesota, 2008.

Smoothing splines are useful tools in nonparametric density estimation. Existing methods for smoothing spline density estimation are often constructed by maximizing the penalized log-likelihood and they need to solve non-linear systems by iterative procedures. In this thesis I propose a nonparametric density estimator that is based on minimizing a penalized L 2 distance. I embed the minimization problem in a reproducing kernel Hilbert space framework in which the solution can be readily calculated. Compared with existing methods, the proposed method is mathematically simple and computationally efficient.

ISBN: 9780549790617Subjects--Topical Terms:

1018410
Applied Mechanics.

Statistical properties of Gaussian reproducing kernel in density estimation.
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005 20110110132554.5
008 130515s2008 ||||||||||||||||| ||eng d
020 $a 9780549790617
035 $a (UMI)AAI3325302
035 $a AAI3325302
040 $a UMI $c UMI
100 1 $a Dong, Hua. $3 1669606
245 1 0 $a Statistical properties of Gaussian reproducing kernel in density estimation.
300 $a 74 p.
500 $a Source: Dissertation Abstracts International, Volume: 69-09, Section: B, page: 5506.
500 $a Adviser: Xiaotong Shen.
502 $a Thesis (Ph.D.)--University of Minnesota, 2008.
520 $a Smoothing splines are useful tools in nonparametric density estimation. Existing methods for smoothing spline density estimation are often constructed by maximizing the penalized log-likelihood and they need to solve non-linear systems by iterative procedures. In this thesis I propose a nonparametric density estimator that is based on minimizing a penalized L 2 distance. I embed the minimization problem in a reproducing kernel Hilbert space framework in which the solution can be readily calculated. Compared with existing methods, the proposed method is mathematically simple and computationally efficient.
520 $a In this thesis I also study the statistical properties of the Gaussian reproducing kernel. The method of regularization with the Gaussian reproducing kernel is popular in machine learning literature and successful in many practical applications. I give the exact eigen-decomposition of the Gaussian reproducing kernel, and by using this result, I show that in the settings of univariate density estimation, in function spaces of very smooth functions, such as the infinite-order Sobolev spaces, the method under consideration yields a convergence rate of Olognn . Simulations are performed to study the finite sample properties of the estimator.
520 $a Finally I extend the results to multivariate density estimation with the Gaussian reproducing kernel and give the exact eigen-decomposition of the multivariate Gaussian reproducing kernel. I also show that in function spaces of very smooth functions, the convergence rate of the proposed method is O1n&parl0;log n&parr0;d, where d is the dimension of the space.
590 $a School code: 0130.
650 4 $a Applied Mechanics. $3 1018410
650 4 $a Mathematics. $3 515831
650 4 $a Statistics. $3 517247
690 $a 0346
690 $a 0405
690 $a 0463
710 2 $a University of Minnesota. $b Statistics. $3 1269982
773 0 $t Dissertation Abstracts International $g 69-09B.
790 1 0 $a Shen, Xiaotong, $e advisor
790 1 0 $a Meeden, Glen $e committee member
790 1 0 $a Oehlert, Gary $e committee member
790 1 0 $a Pan, Wei $e committee member
790 $a 0130
791 $a Ph.D.
792 $a 2008
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3325302