A robust approach to partly linear autoregressive models

BIANCO, ANA; BOENTE, GRACIELA

ESTADISTICA (SANTIAGO DE CHILE)

Instituto Interamericano de Estadística

Año: 2002 vol. 54 p. 249 - 287

0014-1135

This paper first reviews existing procedures to estimate the autoregression function through a kernel $p-$dimensional smoother and recalls their properties under different mixing conditions. Both linear and M-smoothers are considered. In the last years, to solve the curse of dimensionality, there has been an increasing interest in the area of partly linear models. This article also provides an up-to-date presentation of the existing literature on partly linear autoregression. The sensitivity to outliers of the classical estimates for these models is good evidence that robust methods are needed. The problem of obtaining a family of robust estimates, in a partly linear autoregression model, is then addressed introducing a three-step robust procedure. Through a Monte Carlo study, the performance of the proposed estimates is compared with the classical ones. This study shows the advantage of considering the three-step robust estimates based on nearest neighbor with kernel M-smoothers.$p-$dimensional smoother and recalls their properties under different mixing conditions. Both linear and M-smoothers are considered. In the last years, to solve the curse of dimensionality, there has been an increasing interest in the area of partly linear models. This article also provides an up-to-date presentation of the existing literature on partly linear autoregression. The sensitivity to outliers of the classical estimates for these models is good evidence that robust methods are needed. The problem of obtaining a family of robust estimates, in a partly linear autoregression model, is then addressed introducing a three-step robust procedure. Through a Monte Carlo study, the performance of the proposed estimates is compared with the classical ones. This study shows the advantage of considering the three-step robust estimates based on nearest neighbor with kernel M-smoothers.