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Statistical properties of Gaussian r...

Dong, Hua.

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Statistical properties of Gaussian reproducing kernel in density estimation.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Statistical properties of Gaussian reproducing kernel in density estimation./
作者:	Dong, Hua.
面頁冊數:	74 p.
附註:	Source: Dissertation Abstracts International, Volume: 69-09, Section: B, page: 5506.
Contained By:	Dissertation Abstracts International69-09B.
標題:	Applied Mechanics. -
電子資源:	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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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
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773 0 $t Dissertation Abstracts International $g 69-09B.
790 1 0 $a Shen, Xiaotong, $e advisor
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790 1 0 $a Oehlert, Gary $e committee member
790 1 0 $a Pan, Wei $e committee member
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