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Some properties of gamma kernel estimators for small size samples. (Quelques propriétés des estimateurs à noyaux gamma pour des échantillons de petites tailles.) (French. English summary) Zbl 1327.62236

Summary: In this paper, we study the nonunit mass of the gamma (gamma and the modified gamma) kernels estimator for the finite samples. For this, we propose to use the normalization approach (Macro-normalization and the Micro-Normalization) to correct the problem of the non-consistency. In the aim to illustrate the necessity of the normalization approach a detailed simulation study investigates the local and global performances of the considered estimators. The obtained results show the good performances of the normalized gamma kernels estimators.

MSC:

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62M05 Markov processes: estimation; hidden Markov models
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Full Text: Euclid