A sequential procedure for estimating the regression parameter $\beta \in R^k$ in a regression model with symmetric errors is proposed. This procedure is shown to have asymptotically smaller regret than the procedure analyzed by Martinsek when $\mathbf{\beta} = \mathbf{0}$, and the same asymptotic regret as that procedure when $\mathbf{\beta} \neq \mathbf{0}$. Consequently, even when the errors are normally distributed, it follows that the asymptotic regret can be negative when $\mathbf{\beta} = \mathbf{0}$. These results extend a recent work of Takada dealing with the estimation of the normal mean, to both regression and nonnormal cases.
Publié le : 1992-09-14
Classification:
Sequential procedure,
regression,
least squares estimate,
regret,
stopping rule,
62L12,
60G40,
62J05
@article{1176348777,
author = {Sriram, T. N.},
title = {An Improved Sequential Procedure for Estimating the Regression Parameter in Regression Models with Symmetric Errors},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 1441-1453},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348777}
}
Sriram, T. N. An Improved Sequential Procedure for Estimating the Regression Parameter in Regression Models with Symmetric Errors. Ann. Statist., Tome 20 (1992) no. 1, pp. 1441-1453. http://gdmltest.u-ga.fr/item/1176348777/