Subseries Methods in Regression

Abstract

We extend subseries methods for stationary sequences to the regression setting. To estimate sampling distributions, the subseries approach computes the statistic of interest on all possible subseries of a shorter length than the original series, and uses the distribution of these replicates to mimic the distribution of the original statistic. For proper choice of subseries length, the regression parameters can be estimated to order O ( n -2/3 ), thus improving on the normal approximation. The replicates can also be used to reduce the bias of robust estimators. Simulation results demonstrate the finite-sample effectiveness of the approach for both distribution function estimation and bias reduction. Applications to spatial data are also discussed.