非线性回归模型中的约束拟似然

在非线性回归模型中,拟得分函数是一类线性无偏估计函数中的最优者(GodambeandHeyde(1987),朱仲义(1996)),而由拟得分函数得到的拟似然估计在由线性无偏估计函数得到的估计类中具有渐近最优性(林路(1999)).本文则研究非线性回归模型中的有偏估计函数理论,构造了参数的约束拟似然估计,得到了约束拟似然的局部最优性,局部改进了拟似然估计,从而扩充了线性模型中的有偏估计理论.

Constrained Quasi Likelihood in Nonlinear Regression Model

It is well known that in the nonlinear regression models, the quasi score functions is the optimal estimating function in a class of linear unbiased estimating functions (Godambe Heyde(1987),Zhu Zhongyi(1996) and the quasi likelihood estimation obtained from the quasi score function is asymptotically the optimal estimation in a class of estimations obtained from a class of linear unbiased estimating functions (Liu Lu(1999)). To improve the quasi likelihood, in this paper a theory of biased estimating function is introduced, a constrained quasi likelihood estimation is defined and its partial superiority over quasi likelihood is proved. As a result, the constrained quasi likelihood of nonlinear regression model is believed to the developed from the theory of biased estimation in the linear model.