Adaptive estimation of densities of mixture components. (Ukrainian, English) Zbl 1150.62343

Pohyl’ko, D. I.

Teor. Jmovirn. Mat. Stat. 74, 129-142 (2006); translation in Theory Probab. Math. Stat. 74, 147-162 (2007).

Using a wavelet basis the author constructs projective estimates of the density of mixture components in the case where the observations are a sample from a mixture with variable concentrations. The behaviour of threshold nonlinear estimates is studied, when the densities of components belong to Besov spaces. For linear estimates the rate of convergence in the uniform norm is established and the probability of large deviations in this norm is estimated.

Reviewer: Aleksandr D. Borisenko (Kyïv)

MSC:

62G07	Density estimation
42C40	Nontrigonometric harmonic analysis involving wavelets and other special systems
60F10	Large deviations
62G20	Asymptotic properties of nonparametric inference

Keywords:

wavelet basis; threshold estimates; linear estimates; large deviations