DeepAI AI Chat
Log In Sign Up

An RKHS-Based Semiparametric Approach to Nonlinear Sufficient Dimension Reduction

by   Wenquan Cui, et al.

Based on the theory of reproducing kernel Hilbert space (RKHS) and semiparametric method, we propose a new approach to nonlinear dimension reduction. The method extends the semiparametric method into a more generalized domain where both the interested parameters and nuisance parameters to be infinite dimensional. By casting the nonlinear dimensional reduction problem in a generalized semiparametric framework, we calculate the orthogonal complement space of generalized nuisance tangent space to derive the estimating equation. Solving the estimating equation by the theory of RKHS and regularization, we obtain the estimation of dimension reduction directions of the sufficient dimension reduction (SDR) subspace and also show the asymptotic property of estimator. Furthermore, the proposed method does not rely on the linearity condition and constant variance condition. Simulation and real data studies are conducted to demonstrate the finite sample performance of our method in comparison with several existing methods.


page 1

page 2

page 3

page 4


Fréchet Sufficient Dimension Reduction for Random Objects

We in this paper consider Fréchet sufficient dimension reduction with re...

A new reproducing kernel based nonlinear dimension reduction method for survival data

Based on the theories of sliced inverse regression (SIR) and reproducing...

Gradient-based kernel dimension reduction for supervised learning

This paper proposes a novel kernel approach to linear dimension reductio...

A dimension reduction framework for personalized dose finding

The discovery of individual dose rules (IDRs) in personalized medicine i...

A novel extension of Generalized Low-Rank Approximation of Matrices based on multiple-pairs of transformations

Dimension reduction is a main step in learning process which plays a ess...

Bridging linearity-based and kernel-based sufficient dimension reduction

There has been a lot of interest in sufficient dimension reduction (SDR)...

Functional Autoregressive Processes in Reproducing Kernel Hilbert Spaces

We study the estimation and prediction of functional autoregressive (FAR...