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Y. Xia, H. Tong, W. K. Li and L. X. Zhu, “An Adaptive Estimation of Dimension Reduction,” Journal of the Royal Statistical Society, Ser. B, Vol. 64, No. 3, 2002, pp. 363-410. doi:10.1111/1467-9868.03411

has been cited by the following article:

• TITLE: Estimation of Regression Model Using a Two Stage Nonparametric Approach

  AUTHORS: Desale Habtzghi, Jin-Hong Park

  KEYWORDS: Dimension Reduction; Central Subspace; Polynomial Regression; Shape Restricted

  JOURNAL NAME: Applied Mathematics, Vol.4 No.8, August 1, 2013

  ABSTRACT: Based on the empirical or theoretical qualitative information about the relationship between response variable and covariates, we propose a new approach to model polynomial regression using a shape restricted regression after estimating the direction by sufficient dimension reduction. The purpose of this paper is to illustrate that in the absence of prior information other than the shape constraints, our approach provides a flexible fit to the data and improves regression predictions. We use central subspace to estimate the directions and fit a final model by shape restricted regression, when the shape is known or is stipulated from empirical inspection. Comparisons with an alternative nonparametric regression are included. Simulated and real data analyses are conducted to illustrate the performance of our approach.