Data-Based Resolution Selection in Positive Wavelet Density Estimation

Abstract

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.

Key Words:

• Integrated mean square error
• Positive wavelet density estimator
• Wavelet resolution level

Mathematics Subject Classification:

• Primary 62G07
• Secondary 62G20

Acknowledgments