Консистентність оцінок Коенкера-Бассетта в лінійній моделі регресії

Abstract

Asymptotic properties of Koenker - Bassett estimators of linear regression model parameters with discrete observation time and random noise being nonlinear local transformation of Gaussian stationary time series with singular spectrum are studied. The goal of the work lies in obtaining the requirements to regression function and time series that simulates the random noise, under which the Koenker - Bassett estimators of regression model parameters are consistent. Linear regression model with discrete observation time and bounded open convex parametric set is the object of the studying. For the first time in linear regression model with described stationary time series as noise having singular spectrum, the weak consistency of unknown parameters Koenker - Bassett estimators are obtained. For getting these results complicated concepts of time series theory and time series statistics have been used, namely: local transformation of Gaussian stationary time series, stationary time series with singular spectral density, expansions by Chebyshev - Hermite polynomials of the transformed Gaussian time series values.