Maximum likelihood estimation in regression with uniform errors

Abstract

The simple linear regression model y -α + 3x + ε with i i.d uniform errors is considered, and some properties of the maximum likelihood estimators (MLE f s) of α and 3 are derived.In particular, the asymptotic mean square error of the MLE of 3 when α is known to be zero is proportional to (Σ |x |) instead of to (Σ x ) as it is for the usual least squares estimator (LSE) .The MLE's are also superefficient compared with the LSE's when both α and 3 are unknown.1. Introduction.Consider the simple linear regression model with i.i.d.errors (1.1) y jL = α + 3x ± + e ± , i-1,2,..., where we are interested in estimating the parameters α and 3.The usual LSE f s of α and 3 are MLE f s when the ε. are normal, but not when the normality assumption fails to hold.We shall obtain some properties of MLE's when