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 matrix may become singular when an SNP model is overparameterized. This singularity problem may occur even when a model selection criterion penalizes the size of a model, and thus cause problems in the sieves expansion model selection process. We propose to use the likelihood ratio test to safeguard against such overparameterization.