Data-Based Resolution Selection in Positive Wavelet Density Estimation
Jugal K. Ghorai, Dong Yu · Communication in Statistics- Theory and Methods · 2004
The problem of automatic resolution selection for positive wavelet density estimators is considered. Asymptotic formulae for the integrated mean square error (IMSE) of positive wavelet density estimators are derived under a very mild condition on the density function f. Using the formula for IMSE, an asymptotically optimal empirical resolution selection rule is given. The consistency of the density estimator with estimated resolution is also proved.