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 f̌n(x) is proposed which uses kernel‐density and deconvolution techniques. The estimator f̌n(x) is shown to be uniformly consistent, and its appearance and properties are affected by constantsMnandhnwhich the user may choose. The optimal choices ofMnandhndepend on the sample sizen, the noise distribution, and the true distribution which is being estimated. Particular selections forMnandhnwhich minimize upper‐bound functions of the mean squared error for f̌n(x) are recommended.