Central Limit Theorem for a Wavelet Estimator of a Probability Density with a Given Weight

Resumo

The problem of estimating a probability density with a given weight is considered. Probability densities of this type arise in different cases, e.g., analyzing order statistics and studying random-size samples in problems of reliability theory, insurance, and other areas. When constructing an estimator, expansion is used with respect to a wavelet basis based on wavelet functions with bounded spectrum. It is proved that the considered estimator is asymptotically normal when the number of terms of the expansion is fixed and growing.