The Annals of Statistics

On Polynomial-Based Projection Indices for Exploratory Projection Pursuit

Peter Hall

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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

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

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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

Hermite functions Legendre polynomials nonparametric density estimation orthogonal series projection pursuit


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

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