NONPARAMETRIC-ESTIMATION OF A MIXING DENSITY VIA THE KERNEL-METHOD

This article presents a method for estimating the latent distribution of a mixture model. The method is motivated by the standard kernel den sity estimation, but instead of using an estimate based on the unobser ved latent variables, it takes the expectation with respect to their d istribution conditional on the data. The resulting estimator is contin uous and hence appropriate when there is a strong belief in the contin uity of the mixing distribution. An asymptotic justification is presen ted, and the associated computational problems are discussed. The meth od is illustrated by an example of fission track analysis in which the density of the age of crystals is estimated.