5

5

12041

Preconditioned Mixed-Type Splitting Iterative Method For Z-Matrices

In this paper, we present the preconditioned mixed-type
splitting iterative method for solving the linear systems, Ax = b,
where A is a Z-matrix. And we give some comparison theorems
to show that the convergence rate of the preconditioned mixed-type
splitting iterative method is faster than that of the mixed-type splitting
iterative method. Finally, we give a numerical example to illustrate
our results.

Z-matrix, mixed-type splitting iterative method, precondition,comparison theorem, linear system.

4

9999966

The Relative Efficiency of Parameter Estimation in Linear Weighted Regression

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.

Linear weighted regression, Relative efficiency,
Mean matrix, Trace.

3

10000672

The Study of Relative Efficiency in Growth Curve Model

In this paper, some relative efficiency have been discussed, including the LSE estimate with respect to BLUE in curve model. Four new kinds of relative efficiency have defined, and their upper bounds have been discussed.

Relative efficiency, LSE estimate, BLUE estimate,
Upper bound, Curve model.

2

10001598

Two New Relative Efficiencies of Linear Weighted Regression

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.

Linear weighted regression, Relative efficiency,
Lower bound, Parameter estimation.

1

10003235

An Estimation of Variance Components in Linear Mixed Model

In this paper, a linear mixed model which has two
random effects is broken up into two models. This thesis gets
the parameter estimation of the original model and an estimation’s
statistical qualities based on these two models. Then many important
properties are given by comparing this estimation with other general
estimations. At the same time, this paper proves the analysis of
variance estimate (ANOVAE) about σ2 of the original model is equal
to the least-squares estimation (LSE) about σ2 of these two models.
Finally, it also proves that this estimation is better than ANOVAE
under Stein function and special condition in some degree.

Linear mixed model, Random effects, Parameter
estimation, Stein function.