On Estimation for Partial Linear Models

• Activity Number: 431
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Sucharita Ghosh*+
• Companies: Swiss Federal Research Institute WSL
• Keywords: semiparametric estimation ; time series ; smoothing ; asymptotics ; long memory ; geophysical applications

Abstract

Consider time series observations y(i), i=1,2,...,n, which satisfy the semiparametric model y(i) = g(t(i)) + b x(i) + e(i). Here, t(i) denotes rescaled time, g is smooth, b is a constant and e(i) has zero mean & finite variance. The primary aim is estimation of b when x(i) = h(t(i)) + u(i), where h is smooth and u(i) has zero mean & finite variance.

Our interest lies in situations where e(i) and u(i) are unknown transformations of some latent Gaussian processes with long memory correlations (Taqqu 1975). Thus in particular, e and u may be non-Gaussian which may be revealed by a test of normality (Epps 1987, Ghosh 2013) applied to the regression residuals. Moreover, nonstationarity and in particular heteroscedastic extensions can also be considered.

We address estimation of the slope parameter b (Speckman 1988, Beran & Ghosh 1998) and derivation of asymptotic properties of the estimator under some broad technical conditions which will be made explicit during the talk. Further computational issues such as bandwidth selection and other problems related to nonparametric curve estimation are also addressed, as well as some applications.