Functional estimation : Probability density estimation using the kernel method

Probability density estimation using the kernel method
Functional estimation

Author : Denis BOSQ

Publication date: October 10, 2009 | Lire en français

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4. Probability density estimation using the kernel method

Density function estimation plays a central role in functional estimation; the problem is difficult and the applications are numerous.

The situation is as follows: we observe independent real random variables X₁,..., X_n with the same law μ of unknown density f, so we have :

P (a \leq X_{i} \leq b) = μ ([a, b]) = \int_{a}^{b} f (x) d x,

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Probability density estimation using the kernel method

(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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