Estimating Conditional Variance Functions Nonparametrically Using Asymmetric Least Squares

• Activity Number: 400
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yuwen Gu*+
• Companies: University of Minnesota
• Keywords: Nonparametric ; Conditional variance ; Asymmetric least squares ; Local polynomials ; Asymptotic properties ; Heteroscedasticity

Abstract

Asymmetric least squares method allows us to investigate the lower part as well as the upper part of the conditional distribution of a response variable given a set of covariates. More often than not, the variance function, not just the mean function of this conditional distribution, is of interest to us. In a setting where no parametric model is assumed between the response variable and the covariates, we propose the asymmetric least squares approach using local polynomials to estimate the so called conditional expectiles and develop their asymptotic properties under mild conditions. These conditional expectiles are then used to estimate the conditional variance function of the response variable given the covariates. By this non-parametric approach, the variance function is allowed to vary with covariates and can be estimated locally. We show that this method can estimate very well even when heteroscedasticity exists in the data. This is of particular interest in some econometric studies, where the main focus is on measuring the volatility or risk in finance. We give some simulation examples that demonstrate the good performance of our method.