OVERPARAMETERIZATION IN THE SEMINONPARAMETRIC DENSITY-ESTIMATION

The seminonparametric (SNP) density estimation proposed by Gallant and Nychka (1987) and Gallant and Tauchen (1989) has been applied in many econometric analyses. In this paper, we show that the information mat rix may become singular when an SNP model is overparameterized. This s ingularity problem may occur even when a model selection criterion pen alizes the size of a model, and thus cause problems in the sieves expa nsion model selection process. We propose to use the likelihood ratio test to safeguard against such overparameterization. (C) 1998 Elsevier Science S.A.