A note on density estimation for binary sequences

A histogram estimate of the Radon–Nikodym derivative of a probability measure with respect to a dominating measure is developed for binary sequences in {0,1}N. A necessary and sufficient condition for the consistency of the estimate in the mean-square sense is given. It is noted that the product topology on {0,1}N and the corresponding dominating product measure pose considerable restrictions on the rate of sampling required for the requisite convergence.