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研究生:陳興進
研究生(外文):Chen, Shing-Jin
論文名稱:多變量迴歸樣條
論文名稱(外文):Multivariate Regression Splines
指導教授:陳鄰安陳鄰安引用關係
指導教授(外文):Chen, Lin-An
學位類別:碩士
校院名稱:國立交通大學
系所名稱:統計所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:1999
畢業學年度:87
語文別:英文
論文頁數:25
中文關鍵詞:樣條迴歸樣條
外文關鍵詞:SplineRegression Splinelocal supportB-spline
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介紹在非一致平滑條件之下的多變量樣條以及用具有local support的多變量的B-Spline基底來發展這一個樣條空間。並提供這個樣條空間的模擬結果。

A multivariate spline of nonuniform smoothness condition is introduced and a multivariate B-spline basis of local support is developed for this spline space. Simulation results for these splines are provided.

1 Introduction 1
2 Multivariate Regression Spline of
Nonuniform Smoothness Condition 3
3 Multivariate Spline Space 8
4 Simulation for Bivariate Regression Spline 10
4.1 Introduction of Simulation 10
4.2 Simulation 12
4.3 Remarks 15
5 Appendix 16

[1] De Boor, C. (1978), A practical guide to splines, New York: Springer-Verlag.
[2] Buse, A. and Lim, L. (1977), Cubic splines as a special case of restricted least squares, Journal of the American Statistical Association, 72 64-68.
[3] Chen, L.-A. (1996), Bivariate regression splines, Computational Statistics and Data Analysis, 21 399-418.
[4] Chen, L.-A. (1997), Multivariate regression splines, Computational Statistics and Data Analysis, 26 71-82.
[5] Cleveland, W. S. and Devlin, S. J. (1988), Locally weighted regression: an approach to regression analysis by local fitting, Journal of the American Statistical Association, 83 596-610.
[6] Cleveland, W. S., Mallows, C. L. and McRae, J. E. (1993), ATS Methods: Nonparametric regression for non-Gaussian data, Journal of the American Statistical Association, 88 821-835.
[7] Curry, H. B. and Schoenberg, I. J. (1947), On spline distributions and their limits: the Polya distribution functions, Abstract 380t, Bulletion American Mathematical Society, 53, 1114, p109.
[8] Eubank, R. L. (1984), Approximate Regression Models and Splines, Communications in Statistics - Theory and Methods, 13, 433-484.
[9] Eubank, R. L. (1988), Spline smoothing and nonparametric regression, New York: Marcel Dekker, Inc.
[10] Poirier, D. J. (1973), Piecewise regression using cubic splines, Journal of the American Statistical Association, 68 515-524.
[11] Schumaker, L. L. (1984), On Spaces of Piecewise Polynomials in Two Variables. In Singh, S. P. etc.
Approximation Theory and Spline Functions, Reidel, Dodrecht, 151-197.
[12] Smith, P. L. (1979), Splines as a useful and convenient statistical tool, The American Statistician, 33 57-62.
[13] Wahba, G. (1990), Spline Models for Observational Data, Philadelphia: SIAM.
[14] Gunther Nurnberger, Approximation by Spline Functions, Springer-Verlag.

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