A consistent nonparametric density estimator for the deconvolution problem

The problem of nonparametric estimation of a probability density function when the sample observations are contaminated with random noise is studied. A particular estimator f̌ n (x) is proposed which uses kernel‐density and deconvolution techniques. The estimator f̌ n (x) is shown to be uniformly consistent, and its appearance and properties are affected by constants M n and h n which the user may choose. The optimal choices of M n and h n depend on the sample size n , the noise distribution, and the true distribution which is being estimated. Particular selections for M n and h n which minimize upper‐bound functions of the mean squared error for f̌ n (x) are recommended.