This paper gives a class of minimum $L_2$-distance estimators of the autoregression parameter in the first-order autoregression model when the errors have an unknown symmetric distribution. Within the class an asymptotically efficient estimator is exhibited. The asymptotic efficiency of this estimator relative to the least-squares estimator is the same as that of a certain signed rank estimator relative to the sample mean in the one sample location model. The paper also discusses goodness-of-fit tests for testing for symmetry and for a specified error distribution.
@article{1176350059,
author = {Koul, Hira L.},
title = {Minimum Distance Estimation and Goodness-of-Fit Tests in First-Order Autoregression},
journal = {Ann. Statist.},
volume = {14},
number = {2},
year = {1986},
pages = { 1194-1213},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350059}
}
Koul, Hira L. Minimum Distance Estimation and Goodness-of-Fit Tests in First-Order Autoregression. Ann. Statist., Tome 14 (1986) no. 2, pp. 1194-1213. http://gdmltest.u-ga.fr/item/1176350059/