Near optimal thresholding estimation of a Poisson intensity on the real line ∗ Patricia

Abstract: The purpose of this paper is to estimate the intensity of a Poisson process N by using thresholding rules. In this paper, the intensity, defined as the derivative of the mean measure of N with respect to ndx where n is a fixed parameter, is assumed to be non-compactly supported. The estimator f̃n,γ based on random thresholds is proved to achieve the same performance as the oracle estimator up to a possible logarithmic term. Then, minimax properties of f̃n,γ on Besov spaces B p,q are established. Under mild assumptions, we prove that