伴隨時間序列誤差項的非參數模型之估計漸進理論
Asymptotic efficienct estimation in a Nonparametric Regression Model with Autoregressive Moving-average Errors

林財川            

 

摘要/Abstract

本文旨在探討一個可同時解決非常態化、非穩定性和非線性特性的參數模式:Yt = f(Xt) + Zt,其中f(o)表一叢Rd對映到R上的平滑函數,{Xt}為一已知或可觀察的d為度向量序列,{Zt}為一與{Xt}互相獨立的穩定型自我迴歸移動平均序列。本文提出一組較寬鬆且可檢驗的條件,在該條件下證得以 求得許多常見的參數估計能漸進等於在{Zt}為可觀察情況下的結果。

關鍵詞:非常態化、非線性和非穩定型模式;自我相關函數;多項式雲形;自我迴歸移動平均模式:半參數模型;非參數模型



This paper focus on a nonparametric model Yt = f(Xt) + Zt,where f is an unknown smooth function and {Zt} is a sequence of causaland invertible autoregressive moving-average error. We show that undermild assumptions the constructed parametric estimators of error componentare asymptotically equivalent to those based on {Zt}.

Key words and phrases:Autocorrelation function;autoregressive movingaverage model;nonlinear and nonstationary model; nonparametric regression; polynomial spline; semiparametric regression.

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