Square Density Weighted Average Derivatives Estimation of Single Index Models

Abstract

This paper proposes an average derivatives estimator for index coefficients under a single index model, which does not require restrictive conditions such as zero boundary density or density trimming that are often adopted in previous studies including Powell, Stock, and Stoker (1989, PSSE) and Hurdle and Stoker (1989, HSE), among others. Coefficients are consistently estimable by nonparametric mean regression with square density weighted average derivatives (SWADE). Relaxed requirements for SWADE allow more general applications. The asymptotic distribution of SWADE is equivalent in precision to the aforementioned average derivatives estimators (PSSE and HSE). Monte Carlo simulations show that SWADE outperforms HSE in finite sample but is slightly and weakly outweighed by PSSE. These imply that SWADE allows more flexible applications with relaxed distributional characteristics than PSSE and HSE at the expense of slightly deteriorated behavior in finite sample.