Izvorni znanstveni članak
https://doi.org/10.64785/mc.31.1.8
Optimal convergence rates of wavelet estimators for a hidden density in a mixture model
Junke Kou
; School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, China
*
Dan Liang
; School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, China
* Dopisni autor.
Sažetak
his paper investigates nonparametric estimations of a density function in a mixture model. Firstly, a lower
bound estimation under \( L^{p}(1\leq p< +\infty )\) error of an arbitrary density estimator is discussed. Secondly, a linear
estimator and an adaptive nonlinear estimator of the unknown density function are constructed by the wavelet method.
The rates of convergence of those two wavelet estimators are discussed with some mild conditions. Combining with the
lower bound estimations, two wavelet estimators can attain the optimal convergen
Ključne riječi
nonparametric estimation; density function; mixture model; \( 𝐿^{p}\) risk
Hrčak ID:
345981
URI
Datum izdavanja:
2.4.2026.
Posjeta: 244 *