Functional estimation : Density estimation by projection

Density estimation by projection
Functional estimation

Author : Denis BOSQ

Publication date: October 10, 2009 | Lire en français

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5. Density estimation by projection

We now give some indications of a global method for estimating f. The principle is to develop f as a series of orthogonal functions and to estimate the coefficients of this development using empirical averages. We begin with an important special case.

Trigonometric series

On the interval [0,1], the orthonormal system of trigonometric functions is defined by e₀(x) = 1 and $e_{2 j - 1} (x) = \sqrt{2} \sin (2 π jx)$ ,

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Bibliography

(1) - BERLINET (A.), DEVROYE (L) - A comparison of kernel density estimates - Publ. Inst. Statist. Univ. Paris, 38 (3), p. 3-59 (1994).
(2) - BLANKE (D.), PUMO (B.) - Optimal sampling for density estimation in continuous time - J. Time Ser. Anal., 24 (1), p. 1-24...

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Density estimation by projection Functional estimation

5. Density estimation by projection

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Density estimation by projection
Functional estimation