ROBUST REGRESSION AND INTERPOLATION FOR TIME SERIES

1 January 1981

journal article
Published by Wiley in Journal of Time Series Analysis

Vol. 2 (1) , 53-62
https://doi.org/10.1111/j.1467-9892.1981.tb00311.x

Abstract

In this paper we shall consider the interpolation problem under the condition that the spectral density of a stationary process concerned is vaguely known (i.e., Huber's ε ‐contaminated model). Then we can get a minimax robust interpolator for the class of spectral densities S={ g:g(x)=(1‐ε)f(x)+εh(x)ε Ar D_o, 0<εf(x) is a known spectral density and D₀ is a certain class of spectral densities. Also we shall consider the time series regression problem under the condition that the residual spectral density is vaguely known. Then we can get a minimax robust regression coefficient estimate for the class of the residual spectral densities S.

Keywords

This publication has 3 references indexed in Scilit:

Robust Linear Extrapolations of Second-order Stationary Processes
The Annals of Probability, 1978
Multiple Time Series
Wiley Series in Probability and Statistics, 1970
Robust Estimation of a Location Parameter
The Annals of Mathematical Statistics, 1964