The Annals of Statistics
- Ann. Statist.
- Volume 17, Number 2 (1989), 589-605.
On Polynomial-Based Projection Indices for Exploratory Projection Pursuit
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 . 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.
Ann. Statist., Volume 17, Number 2 (1989), 589-605.
First available in Project Euclid: 12 April 2007
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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