On Gauss quadrature and partial cross validation

A. S. Kozek; J. Yin

doi:10.1016/S0167-9473(03)00040-9

On Gauss quadrature and partial cross validation

A. S. Kozek^*, J. Yin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

New estimators of expected values Ew(X) of functions of a random variable X are introduced. The new estimators are based on Gauss quadrature, a numerical method frequently used to approximate integrals over finite intervals. The estimators need a small number of numerical evaluations and hence are useful in partial cross validation (PCV) a numerical method for finding optimal smoothing parameters in nonparametric curve estimation. The PCV can considerably reduce the computational cost of the generalized cross validation method typically used to determine the optimal smoothing parameter.

Original language	English
Pages (from-to)	431-448
Number of pages	18
Journal	Computational Statistics and Data Analysis
Volume	45
Issue number	3
DOIs	https://doi.org/10.1016/S0167-9473(03)00040-9
Publication status	Published - 10 Apr 2004

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keywords = "Asymptotic distributions, Cross-validation, Fast statistical methods, Gauss quadrature, Nonparametric regression, Smoothing",

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AB - New estimators of expected values Ew(X) of functions of a random variable X are introduced. The new estimators are based on Gauss quadrature, a numerical method frequently used to approximate integrals over finite intervals. The estimators need a small number of numerical evaluations and hence are useful in partial cross validation (PCV) a numerical method for finding optimal smoothing parameters in nonparametric curve estimation. The PCV can considerably reduce the computational cost of the generalized cross validation method typically used to determine the optimal smoothing parameter.

KW - Asymptotic distributions

KW - Cross-validation

KW - Fast statistical methods

KW - Gauss quadrature

KW - Nonparametric regression

KW - Smoothing

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JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

IS - 3

ER -

On Gauss quadrature and partial cross validation

Abstract

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