Open Science Research Excellence

Baoguang Tian

Publications

5

Publications

5
12041
Preconditioned Mixed-Type Splitting Iterative Method For Z-Matrices
Abstract:
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.
Keywords:
Z-matrix, mixed-type splitting iterative method, precondition,comparison theorem, linear system.
4
9999966
The Relative Efficiency of Parameter Estimation in Linear Weighted Regression
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.

Keywords:
Linear weighted regression, Relative efficiency, Mean matrix, Trace.
3
10000672
The Study of Relative Efficiency in Growth Curve Model
Abstract:

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.

Keywords:
Relative efficiency, LSE estimate, BLUE estimate, Upper bound, Curve model.
2
10001598
Two New Relative Efficiencies of Linear Weighted Regression
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.
Keywords:
Linear weighted regression, Relative efficiency, Lower bound, Parameter estimation.
1
10003235
An Estimation of Variance Components in Linear Mixed Model
Abstract:
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.
Keywords:
Linear mixed model, Random effects, Parameter estimation, Stein function.