M-estimation of linear models with dependent errors

Abstract

We study asymptotic properties of $M$-estimates of regression parameters in linear models in which errors are dependent. Weak and strong Bahadur representations of the $M$-estimates are derived and a central limit theorem is established. The results are applied to linear models with errors being short-range dependent linear processes, heavy-tailed linear processes and some widely used nonlinear time series.

Published at http://dx.doi.org/10.1214/009053606000001406 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• On the Bahadur representation of sample quantiles for dependent sequences
• M-estimation of linear models with dependent errors
• Empirical processes of dependent random variables

Cited by in corpus (11)

• M-estimation of linear models with dependent errors
• Local linear quantile estimation for nonstationary time series
• Nonparametric inference of quantile curves for nonstationary time series
• Robust Spectral Analysis
• The Generalized Method of Wavelet Moments with Exogenous Inputs: a Fast Approach for the Analysis of GNSS Position Time Series
• Quantile Fourier Transform, Quantile Series, and Nonparametric Estimation of Quantile Spectra
• Robust optimal estimation of location from discretely sampled functional data
• Asymptotic distribution of least square estimators for linear models with dependent errors
• M-estimation in high-dimensional linear model
• Spline Autoregression Method for Estimation of Quantile Spectrum
• Sequential Monitoring of Changes in Housing Prices