導函數不連續型態迴歸函數之非參數估計

ON ESTIMATING REGRESSION FUNCTION WITH CHANGE POINTS

蕭光呈(Kuang-Chen Hsiao)

指導教授 ： 鄭明燕

國立臺灣大學/理學院/數學研究所/碩士(2005年)

https://doi.org/10.6342/NTU.2005.00238

摘要

無資料

關鍵字

不連續點 ； 迴歸函數 ； 無母數 ； 尖點 ； 導函數不連續

並列摘要

Local polynomial fitting has been known as a powerful
nonparametric regression method when dealing with correlated data and when trying to find implicit connections between variables. This method relaxes
assumptions on the form of the regression function under investigation. Nevertheless, when we try fitting a regression curve with precipitous changes using general local polynomial method, the fitted curve is oversmoothed near points where the true regression function has sharp features. Since local polynomial modelling is fitting a "polynomial", a continuous and smooth function, to the regression function at each point of estimation, such drawback is intrinsic. Here, we suggest a modified estimator of the conventional local polynomial method. Asymptotic mean squared error is derived. Several numerical results are also presented.

並列關鍵字

jump ； regression function ； nonparametric ； cusp ； discontinuity

參考文獻

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J.Fan and I.Gijbels. (1996). Local Polynomial Modelling and Its Applications. Chapman&Hall, London.

Loader, C.R. (1994). Change point estimation using nonparametric regression. AT&T Bell Laboratories.

Müller, H.G. (1992). Change-points in nonparametric regression analysis. The Annals of Statistics 20 737-761.

Nason, G.P.and Silverman, B.W. (1994). The discrete wavelet transform in S. J.Comput.Graph.Statist. 3 163-191.