Asymptotic Efficiency in a Partly Autoregressive Model
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摘要: 本文考虑部分自回归模型Xt = Xt-1β+g（Ut） + εi,t≥1.这里g是一未知函数,β是一待估参数εj是具有0均值和方差σ2的i.i.d.误差,Ut i.i.d.服从[0,1]上均匀分布.本文首先给出了相合估计的收敛阶和Takeuchi意义下渐近有效界.同时给出了β最小二乘估计是有效的充要条件.最后证明了MLE是渐近有效的。Abstract: Consider the model Xt = Xt-1β+g（Ut）+ εi for t≥ 1. Here g is an unknown function, β is an unknown parameter to be estimated and εj are i.i d. with mean 0 and variance σ2 and Ut are i.i.d. random variables obeyed uniformly on {0, l} The order of convergence of consistent estimators and the bound of asymptotic efficiency in sense of Takeuchi are given. Meanwhile we give a necessary and sufficient condition that the least squares of β is asymptotically efficient, and we also show that the MLE is asymptotically efficient.
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