鄭明燕臺灣大學：數學研究所蕭光呈Hsiao, Kuang-ChenKuang-ChenHsiao2007-11-282018-06-282007-11-282018-06-282005http://ntur.lib.ntu.edu.tw//handle/246246/59417Local 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.Introduction.............................................1 Overview of Several Existing Methods.....................2 Müller (1992). Two one-sided kernel type estimators......3 Qiu and Yandell (1998). Jump detection procedure.........4 Qiu (2003). Jump-preserving estimator....................5 Methodology..............................................6 Derivation of the jump-preserving estimator..............6 Assumptions..............................................6 Notations................................................7 Jump-preserving estimator................................8 Theoretical results......................................9 Numerical Study..........................................12 Discussion...............................................13 References...............................................23375716 bytesapplication/pdfen-US不連續點迴歸函數無母數尖點導函數不連續jumpregression functionnonparametriccuspdiscontinuitythesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59417/1/ntu-94-R92221015-1.pdf