Dimension reduction in spatial regression with kernel SAVE method

Mètolidji Moquilas Raymond Affossogbe,Carlos Ogouyandjou,Guy Martial Nkiet

doi:10.5802/crmath.187

Abstract

We consider the smoothed version of sliced average variance estimation (SAVE) dimension reduction method for dealing with spatially dependent data that are observations of a strongly mixing random field. We propose kernel estimators for the interest matrix and the effective dimension reduction (EDR) space, and show their consistency.

Highlights

Let us consider the semiparametric regression model introduced by Li [8] and defined asY = g, (1)where Y
Rd, d ≥ 2), N is an integer such that N < d, the parameters β1, β2, . . . , βN are d -dimensional linearly independent vectors, ε is a random variable that is independent of X, and g is an arbitrary unkown function
Nonparametric statistical methods have evolved with the existence of spatially dependent data

Summary

Introduction

Let us consider the semiparametric regression model introduced by Li [8] and defined as. The estimation of the space spanned by the βk ’s, called the effective dimension reduction (EDR) space, is a crucial issue for achieving reduction dimension For this problem, Li [8] introduced the Sliced Inverse Regression (SIR) method whereas an alternative method, called sliced average variance estimation (SAVE), that is more comprehensive since it uses first and second moments was proposed in [4]. Li [8] introduced the Sliced Inverse Regression (SIR) method whereas an alternative method, called sliced average variance estimation (SAVE), that is more comprehensive since it uses first and second moments was proposed in [4] Smoothed versions of these methods, based on kernel estimators, have been proposed later in [13] and [14].

Kernel estimation of SAVE based on spatial data

Assumptions and asymptotic results

Outline of proofs