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Comparison of two orthogonal series methods of estimating a density and its derivatives on an interval

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  • Hall, Peter

Abstract

We compare the merits of two orthogonal series methods of estimating a density and its derivatives on a compact interval--those based on Legendre polynomials, and on trigonometric functions. By examining the rates of convergence of their mean square errors we show that the Legendre polynomial estimators are superior in many respects. However, Legendre polynomial series can be more difficult to construct than trigonometric series, and to overcome this difficulty we show how to modify trigonometric series estimators to make them more competitive.

Suggested Citation

  • Hall, Peter, 1982. "Comparison of two orthogonal series methods of estimating a density and its derivatives on an interval," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 432-449, September.
    • Handle: RePEc:eee:jmvana:v:12:y:1982:i:3:p:432-449
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    Cited by:

    1. Im, Jongho & Morikawa, Kosuke & Ha, Hyung-Tae, 2020. "A least squares-type density estimator using a polynomial function," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).

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