Functional estimation : Estimation of the distribution function

Estimation of the distribution function
Functional estimation

Author : Denis BOSQ

Publication date: October 10, 2009 | Lire en français

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3. Estimation of the distribution function

The theoretical distribution function F (Example 2) is associated with the empirical distribution function :

F_{n} (x) = μ_{n} (] - \infty, x]), x \in ℝ

To explain this, we use the notation :

\begin{matrix} 1_{B} (u) = 1, \end{matrix}

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Estimation of the distribution function

(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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