Asymptotic expansion for weighted least squares in linear regression models

Abstract

A studentized weighted least squares estimator in a linear regression model is given, this statistic is proved to be asymptotically normal and can be used in applications, also an asymptotic expansion for the distribution of a standardized weighted least square with weights estimated by replication is given and we will comment on the asymptotic expansion for a studentized weighted least square, these expansions are useful in proving the validity of other procedures.

Keywords:

• Linear models
• weighted least squares
• edgeworth eexpansions