Kavli Affiliate: Wei Gao
| First 5 Authors: Zheng Li, Yunhao Wang, Wei Gao, Hon Keung Tony Ng,
| Summary:
Dimension reduction techniques, such as Sufficient Dimension Reduction (SDR),
are indispensable for analyzing high-dimensional datasets. This paper
introduces a novel SDR method named Principal Square Response Forward
Regression (PSRFR) for estimating the central subspace of the response variable
Y, given the vector of predictor variables $bm{X}$. We provide a computational
algorithm for implementing PSRFR and establish its consistency and asymptotic
properties. Monte Carlo simulations are conducted to assess the performance,
efficiency, and robustness of the proposed method. Notably, PSRFR exhibits
commendable performance in scenarios where the variance of each component
becomes increasingly dissimilar, particularly when the predictor variables
follow an elliptical distribution. Furthermore, we illustrate and validate the
effectiveness of PSRFR using a real-world dataset concerning wine quality. Our
findings underscore the utility and reliability of the PSRFR method in
practical applications of dimension reduction for high-dimensional data
analysis.
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