2. Empirical law

In the sample framework, where X = (X ₁ ,...,X _n ) has as components independent variables of the same law μ, we define the empirical law by posing :

μ_{n} = \frac{1}{n} \sum_{i = 1}^{n} δ_{(X_{i})}

where the notation δ _(a) denotes the "mass" (+ 1) at point a; μ _n is therefore constructed...

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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....

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