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Data-driven shrinkage strategies for quasi-regression.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Data-driven shrinkage strategies for quasi-regression.
Author:	Jiang, Tao.
Description:	90 p.
Notes:	Adviser: Art B. Owen.
Notes:	Source: Dissertation Abstracts International, Volume: 64-09, Section: B, page: 4444.
Contained By:	Dissertation Abstracts International64-09B.
Subject:	Statistics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3104254
ISBN:	0496518224

Data-driven shrinkage strategies for quasi-regression.
Jiang, Tao.

Data-driven shrinkage strategies for quasi-regression. [electronic resource] - 90 p.

Adviser: Art B. Owen.

Thesis (Ph.D.)--Stanford University, 2003.

In this thesis we aim to improve the performance of quasi-regression. To speed up the convergence of the estimates, we incorporate shrinkage parameters into procedures of coefficient estimation and function approximation. Two groups of shrinkage strategies are discussed and comparisons are made on a variety of examples. For black-box functions that have approximately sparse representations in the basis expansion, further enhancements are made with the adaptive basis search algorithm. It selects important basis functions into and removes unessential ones out of the model dynamically, making it possible to explore a even larger basis function set.

ISBN: 0496518224Subjects--Topical Terms:

182057
Statistics.

Data-driven shrinkage strategies for quasi-regression.
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502 $a Thesis (Ph.D.)--Stanford University, 2003.
520 # $a In this thesis we aim to improve the performance of quasi-regression. To speed up the convergence of the estimates, we incorporate shrinkage parameters into procedures of coefficient estimation and function approximation. Two groups of shrinkage strategies are discussed and comparisons are made on a variety of examples. For black-box functions that have approximately sparse representations in the basis expansion, further enhancements are made with the adaptive basis search algorithm. It selects important basis functions into and removes unessential ones out of the model dynamically, making it possible to explore a even larger basis function set.
520 # $a Many statistical models and machine learning algorithms make use of black-box functions, i.e. complex functions depending on many variables in a poorly-understood fashion. Given such a function f(x) for d-dimensional x, it can be important to tell which variables, if any, dominate f and how they affect the function.
520 # $a The functional ANOVA decomposes a square integrable f into a sum of 2d component functions that depend on subsets of input variables. The variances of the component functions can be used to identify important variables and interactions. In quasi-regression the function f is expanded in an orthonormal basis. A large number of the coefficients are estimated by Monte Carlo simulation. The ANOVA component functions of f can be approximated as sums of coefficients times basis functions over certain indices sets. Numerical and graphical interpretation can be performed on the approximations.
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791 $a Ph.D.
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