Data-based optimal smoothing of a wavelet density estimator

The problem of estimating a probability density function based on a complete random sample using a wavelet-based orthogonal expansion is considered. We introduce linear modifications to the empirical wavelet expansion coefficients to control the smoothness of the estimator. A method for estimating the optimal smoothing coefficients from the data is introduced. Finally, we prove that the estimator can achieve the optimal rate of convergence under mean integrated squared error as the sample size tends to infinity.