Asymptotic distributions for testing dimensionality in q-based pHd

R. Dennis Cook; Xiangrong Yin

doi:10.1016/S0167-7152(02)00092-5

Asymptotic distributions for testing dimensionality in q-based pHd

R. Dennis Cook
, Xiangrong Yin

Statistics (Twin Cities)

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

1 Scopus citations

Abstract

We show that the test statistic for dimension in q-based principal Hessian directions (pHd) is distributed as a linear combination of X² random variables. Simpler distributions can result depending on the distribution of the predictors and the adequacy of the quadratic model.

Original language	English (US)
Pages (from-to)	233-243
Number of pages	11
Journal	Statistics and Probability Letters
Volume	58
Issue number	3
DOIs	https://doi.org/10.1016/S0167-7152(02)00092-5
State	Published - Jul 1 2002

Bibliographical note

Funding Information:
This work was supported in part by National Science Foundation Grant DMS-9703777.

Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

Keywords

Asymptotic distribution
Central subspaces
Dimension-reduction subspace
Regression graphics
pHd

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10.1016/S0167-7152(02)00092-5

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abstract = "We show that the test statistic for dimension in q-based principal Hessian directions (pHd) is distributed as a linear combination of X2 random variables. Simpler distributions can result depending on the distribution of the predictors and the adequacy of the quadratic model.",

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AB - We show that the test statistic for dimension in q-based principal Hessian directions (pHd) is distributed as a linear combination of X2 random variables. Simpler distributions can result depending on the distribution of the predictors and the adequacy of the quadratic model.

KW - Asymptotic distribution

KW - Central subspaces

KW - Dimension-reduction subspace

KW - Regression graphics

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JO - Statistics and Probability Letters

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ER -

Asymptotic distributions for testing dimensionality in q-based pHd

Abstract

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Keywords

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