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ERROR ESTIMATES FOR DOMINICI’S HERMITE FUNCTION ASYMPTOTIC FORMULA AND SOME APPLICATIONS

Part of: Nonparametric inference

Published online by Cambridge University Press:  04 December 2009

R. KERMAN ,
M. L. HUANG  and
M. BRANNAN
R. KERMAN
Affiliation:
Department of Mathematics, Brock University, St. Catharines, Ontario, Canada L2S 3A1 (email: mhuang@brockU.CA)
M. L. HUANG*
Affiliation:
Department of Mathematics, Brock University, St. Catharines, Ontario, Canada L2S 3A1 (email: mhuang@brockU.CA)
M. BRANNAN
Affiliation:
Department of Mathematics, Brock University, St. Catharines, Ontario, Canada L2S 3A1 (email: mhuang@brockU.CA)
*
✉For correspondence; e-mail: mhuang@brockU.CA
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Abstract

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The aim of this paper is to find a concrete bound for the error involved when approximating the nth Hermite function (in the oscillating range) by an asymptotic formula due to D. Dominici. This bound is then used to study the accuracy of certain approximations to Hermite expansions and to Fourier transforms. A way of estimating an unknown probability density is proposed.

Keywords

Hermite functionasymptotic formulaGreen’s functionHermite expansionFourier transformdensity estimation

MSC classification

Secondary: 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 62G07: Density estimation

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 4 , April 2009 , pp. 550 - 561
Copyright
Copyright © Australian Mathematical Society 2009

References

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