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 Härdle 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.