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