Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Wavelet Estimation of Regression Functions with Errors in Variables

  • Kim, Woo-Chul (Professor, Department of Computer Science and Statistics, Seoul National University) ;
  • Koo, Ja-Yong (Associate Professor, Department of Statistics, Hallym University)
  • Published : 1999.12.01
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Abstract

This paper addresses the issue of estimating regression function with errors in variables using wavelets. We adopt a nonparametric approach in assuming that the regression function has no specific parametric form, To account for errors in covariates deconvolution is involved in the construction of a new class of linear wavelet estimators. using the wavelet characterization of Besov spaces the question of regression estimation with Besov constraint can be reduced to a problem in a space of sequences. Rates of convergence are studied over Besov function classes $B_{spq}$ using $L_2$ error measure. It is shown that the rates of convergence depend on the smoothness s of the regression function and the decay rate of characteristic function of the contaminating error.

Keywords

References

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