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Partial Dynamic Dimension Reduction for Conditional Mean in Regression

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Abstract

In many regression analysis, the authors are interested in regression mean of response variate given predictors, not its the conditional distribution. This paper is concerned with dimension reduction of predictors in sense of mean function of response conditioning on predictors. The authors introduce the notion of partial dynamic central mean dimension reduction subspace, different from central mean dimension reduction subspace, it has varying subspace in the domain of predictors, and its structural dimensionality may not be the same point by point. The authors study the property of partial dynamic central mean dimension reduction subspace, and develop estimated methods called dynamic ordinary least squares and dynamic principal Hessian directions, which are extension of ordinary least squares and principal Hessian directions based on central mean dimension reduction subspace. The kernel estimate methods for dynamic ordinary least squares and dynamic Principal Hessian Directions are employed, and large sample properties of estimators are given under the regular conditions. Simulations and real data analysis demonstrate that they are effective.

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Authors and Affiliations

  1. School of Electronical and Information Engineering, Fuqing Branch of Fujian Normal University, Fuqing, 350300, China

    Shengjin Gan

  2. School of Statistics, East China Normal University, Shanghai, 200062, China

    Zhou Yu

Authors
  1. Shengjin Gan
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  2. Zhou Yu
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Corresponding author

Correspondence to Zhou Yu.

Additional information

This research was supported by the Natural Science Foundation of Fujian Province of China under Grant No. 2018J01662, and High-Level Cultivation Project of Fuqing Branch of Fujian Normal University under Grant No. KY2018S02.

This paper was recommended for publication by Editor SUN Liuquan.

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Gan, S., Yu, Z. Partial Dynamic Dimension Reduction for Conditional Mean in Regression. J Syst Sci Complex 33, 1585–1601 (2020). https://doi.org/10.1007/s11424-020-8329-3

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  • DOI: https://doi.org/10.1007/s11424-020-8329-3

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