AN IMPROVED SEQUENTIAL PROCEDURE FOR ESTIMATING THE REGRESSION PARAMETER IN REGRESSION-MODELS WITH SYMMETRICAL ERRORS

A sequential procedure for estimating the regression parameter beta is-an-element-of 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 beta = 0, and the same asymptotic regret as that procedure when beta not-equal 0. Consequently, even when the errors are normally distributed, it follows that the asymptotic regret can be negative when beta = 0. These results extend a recent work of Takada dealing with the estimation of the normal mean, to both regression and nonnormal cases.