Wavelet based empirical Bayes estimation for the uniform distribution

The theory of wavelets is a fast developing component in mathematics with great potential in statistical applications. In this work, we incorporate the wavelet tool into the method of empirical Bayes estimation. Asymptotic behavior of the wavelet based empirical Bayes estimator is investigated. The kernel based estimator studied by Nogami (1988) has convergence rate O(n-1/2). We show that the wavelet based empirical Bayes estimator attains the rate O(n-2s/(2s+1)), where s [greater-or-equal, slanted] 1 is the regularity index of the marginal pdf fG. Derivatives considered here are distributional derivatives.