We study the asymptotic properties of semiparametric estimators based on a sample of size n from a distribution belonging to a kernel family with a vector parameter and with an unknown generator. The available information on the generator comes from an independent sample of size m. The natural exponential family(NEF), which includes many distributions that are frequently used in applications, is a special case of the broader class of kernel families. Besides being of theoretical interest, the setup seems a natural model for case-control studies. Our approach consists in replacing the kernel family with its empirical counterpart by replacing the unknown generator with its empirical version. The resulting Empirical Maximum Likelihood Estimator (EMLE) and Empirical Method of Moments Estimator(EMME) are functions of both samples. Their asymptotic properties are explored. Both the EMME and EMLE are consistent and asymptotically normal when properly normalized, where both the normalization factor and the asymptotic covariance matrix depend on the rate of growth of m relative to n.