The Annals of Statistics

On Polynomial-Based Projection Indices for Exploratory Projection Pursuit

Peter Hall

Full-text: Open access

Abstract

We develop asymptotic theory for two polynomial-based methods of estimating orientation in projection pursuit density approximation. One of the techniques uses Legendre polynomials and has been proposed and implemented by Friedman [1]. The other employs Hermite functions. Issues of smoothing parameter choice and robustness are addressed. It is shown that each method can be used to construct $\sqrt n$-consistent estimates of the projection which maximizes distance from normality, although the former can only be employed in that manner when the underlying distribution has extremely light tails. The former can be used very generally to measure "low-frequency" departure from normality.

Article information

Source
Ann. Statist., Volume 17, Number 2 (1989), 589-605.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347127

Digital Object Identifier
doi:10.1214/aos/1176347127

Mathematical Reviews number (MathSciNet)
MR994252

Zentralblatt MATH identifier
0717.62051

JSTOR
links.jstor.org

Subjects
Primary: 62H99: None of the above, but in this section
Secondary: 62H05: Characterization and structure theory

Keywords
Hermite functions Legendre polynomials nonparametric density estimation orthogonal series projection pursuit

Citation

Hall, Peter. On Polynomial-Based Projection Indices for Exploratory Projection Pursuit. Ann. Statist. 17 (1989), no. 2, 589--605. doi:10.1214/aos/1176347127. https://projecteuclid.org/euclid.aos/1176347127


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