A Consistent Estimator for Model Structure and Variable Selection

A kernel-based estimator is proposed for identifying the underlying structure of a nonparametric regression model from a wide range of alternatives known up to second-order derivatives. The estimator with modifications can further select relevant variables in the model. Under mild conditions, the estimator is shown to be consistent for both model structure and variable selection. The estimator is computationally efficient, can be easily deployed on a parallel computing system, and exhibits appealing finite sample performance through simulation studies. An empirical application is given to illustrate how the unknown underlying structure of a production function can be identified in practice.