Nonparametric estimation of a mixing density via the kernel method

We present a method to estimate the latent distribution for a mixture model. Our method is motivated by the standard kernel density estimation but instead of using an estimate based on the unobserved latent variables, we take the expectation with respect to their distribution conditional on the data. The resulting estimator is continuous and, hence, is appropriate when there is a strong belief in the continuity of the mixing distribution. We present an asymptotic justification and we discuss the associated computational problems. The method is illustrated by an example of fission track analysis where we estimate the densi ty of the age of crystals