Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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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.)
  • Published : 1996.12.01
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Abstract

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.

Keywords

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