Journal of the Korean Statistical Society

  • 제25권4호
  • /
  • Pages.499-514
  • /
  • 1996
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

Kernel Regression Estimation for Permutation Fixed Design Additive Models

  • Baek, Jangsun (Department of Statistics, Chonnam National University) ;
  • Wehrly, Thomas E. (Dept. of Statistics, Texas A&M Univ.)
  • 발행 : 1996.12.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Consider an additive regression model of Y on X = (X$_1$,X$_2$,. . .,$X_p$), Y = $sum_{j=1}^pf_j(X_j) + $\varepsilon$$, where $f_j$s are smooth functions to be estimated and $\varepsilon$ is a random error. If $X_j$s are fixed design points, we call it the fixed design additive model. Since the response variable Y is observed at fixed p-dimensional design points, the behavior of the nonparametric regression estimator depends on the design. We propose a fixed design called permutation fixed design, and fit the regression function by the kernel method. The estimator in the permutation fixed design achieves the univariate optimal rate of convergence in mean squared error for any p $\geq$ 2.

키워드

참고문헌

  1. Journal of the American Statistical Association v.80 Estimationg Optimal Transformations for Multiple Regression and Correlation (woth discussiosn) Breiman, L.;Friedman, J. H.
  2. The Annals of Statistics v.17 Linesr Smoothers and Additive Models (with discussion) Buja, A.;Hastie, T.;Tibshirani, R.
  3. Spline Smoothing and Nonparametric Regression Eubank, R. L.
  4. Journal of the American Statistical Association v.87 Design-adaptive nonpartametric regression Fan, J.
  5. Journal of the American Statistical Association v.76 Proection Pursuit Regression Friedman, J. H.;Stuetzle, W.
  6. Smoothing Tecfhniques for Curve Estimation Kernel Estimation of Regression Functions Gasser, T.;Muller, H. G.;T. Gassr(ed.);M. Rosenblatt(ed.)
  7. Statistics and Probadility Letters v.7 Asymptotic Properties of the Multivatiate Nadaraya-Watson Regression Function Estimate Georgiev, A. A.
  8. Statistics and Probadility Letters v.10 Nonparametric Multiple Function Fitting Georgiev, A. A.
  9. Econometric Society Monographs No. 19 Applied Nonparametric Regression Hardle, W.
  10. CORE Discussion paper N9068 How Many Terms Should be Added into an Additive Model" Hardle, W.;Tsybakov, A. B.
  11. Monographs of Statistics and Applied Probility 43 Generalized Additive Models Hastie, T. J.;Tibshirani, R. J.
  12. Journal of the American Statistical Association v.89 Versions of Kernel-Type Regression Ectimators Jones, M. C.;Davies, S. J.;Park, B. U.
  13. Springer Lecture Notes in Statistics Nonpatametric Regression Analysis of Longitudinal Data Muller, H. G.
  14. The Annals of Statistics v.13 Additive Regression and Other Nonparaametric Models Stone, C. J.
  15. Smoothing Techniques for Curve Estimation Convergenece Rates of Thin Plate Smooting Splines When the Data are Noisy Wahba, G.;T. Gasser(eds.);M. Rosenblatt(eds.)
  16. Monographs on Statistics and Applied Probability60 Kernel Smoothing Wand, M. P.;Jones, M. C.