Abstract: In statistics parameter theory, usually the
parameter estimations have two kinds, one is the least-square
estimation (LSE), and the other is the best linear unbiased
estimation (BLUE). Due to the determining theorem of
minimum variance unbiased estimator (MVUE), the parameter
estimation of BLUE in linear model is most ideal. But since
the calculations are complicated or the covariance is not
given, people are hardly to get the solution. Therefore, people
prefer to use LSE rather than BLUE. And this substitution
will take some losses. To quantize the losses, many scholars
have presented many kinds of different relative efficiencies in
different views. For the linear weighted regression model, this
paper discusses the relative efficiencies of LSE of β to BLUE
of β. It also defines two new relative efficiencies and gives
their lower bounds.
Abstract: A new relative efficiency in linear model in reference is
instructed into the linear weighted regression, and its upper and lower
bound are proposed. In the linear weighted regression model, for the
best linear unbiased estimation of mean matrix respect to the
least-squares estimation, two new relative efficiencies are given, and
their upper and lower bounds are also studied.