摘要
考虑Ｙｉ＝Ｘｉτβ＋ｇ（ｔｉ）＋εｉ，１≤ｉ≤ｎ，这里Ｘｉ是一固定设计点列，ｔｉ是独立同分布（ｉ．ｉ．ｄ．）随机变量并且服从［０，１］上均匀分布。εｉ独立同分布且均值为０，方差为σ２＜∞，β和ｇ未知。本文先给出了β的拟最小二乘估计和拟极大似然估计ＭＬ，然后考虑了的渐近正态性和二阶渐近有效性，同时根据ＭＬ构造了β的一个二阶渐近有效估计。
Suppose that Yi=Xiτβ+g(ti)+εi,1≤i≤n,where Xi(k-vectors) are known design points,ti are i.i.d.and obey uniform distribution on[0,1],εi are independent identical random variables with zero means and finite variance σ2.β and g are unknown.Pseudo-LS estimators βand Pseudo-ML estimator βML of β are given.then we investigate asymptotic normality and the second order asymptotic efficiency of β,meanwhile,a class of second order asymptotically efficient based on βML are constructed.
出处
《江西科学》
1995年第1期1-11,共11页
Jiangxi Science
关键词
部分线性模型
渐近正态性
渐近有效性
估计
Partly linear model,Asymptotic normality,Second order asymptotic efficiency
