Title: Intensive comparison of semi-parametric and non-parametric dimension reduction methods in forward regression
Authors: Minju Shin - Ewha Womans University (Korea, South) [presenting]
Jae Keun Yoo - Ewha Womans University (Korea, South)
Abstract: Principal Fitted Component (PFC) is a semi-parametric sufficient dimension reduction (SDR) method. The PFC has a connection with other usual non-parametric SDR methods. The connection is limited to sliced inverse regression and ordinary least squares. Since there is no direct comparison between the two approaches in various forward regressions up to date, practical guidance between the two approaches is necessary for usual statistical practitioners. To fill this practical necessity, we newly derive a connection of the PFC to covariance methods (Yin and Cook, 2002), which is one of the most popular SDR methods. Also, intensive numerical studies have been done closely to examine and compare the estimation performances of the semi- and non-parametric SDR methods for various forward regressions. The founding from the numerical studies is confirmed in a real data example.