We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {(<italic>Y</italic>, <italic>null</italic>)}. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are...

Models with single-index structures are among the many existing popular semiparametric approaches for either the conditional mean or the conditional variance. This paper focuses on a single-index model for the conditional quantile. We propose an adaptive estimation procedure and an iterative...

We examine the higher order asymptotic properties of semiparametric regression estimators that were obtained by the general MINPIN method described in Andrews (1989, Semiparametric Econometric Models: I. Estimation, Discussion paper 908, Cowles Foundation). We derive an order <italic>n</italic>⁻¹ stochastic...

We construct efficient estimators of the identifiable parameters in a regression model when the errors follow a stationary parametric ARCH(<italic>P</italic>) process. We do not assume a functional form for the conditional density of the errors, but do require that it be symmetric about zero. The estimators of...