Estimation in additive models with highly or nonhighly correlated covariates

TL;DR

This paper develops two novel nonparametric estimation methods for additive models with highly or nonhighly correlated covariates, addressing challenges in DNA microarray data and interest rate prediction.

Contribution

It introduces integration and pooled backfitting estimation techniques tailored for different correlation structures among covariates, with proven asymptotic properties.

Findings

Asymptotic normality of estimators established

Simulation results demonstrate finite sample effectiveness

Real data applications show practical utility

Abstract

Motivated by normalizing DNA microarray data and by predicting the interest rates, we explore nonparametric estimation of additive models with highly correlated covariates. We introduce two novel approaches for estimating the additive components, integration estimation and pooled backfitting estimation. The former is designed for highly correlated covariates, and the latter is useful for nonhighly correlated covariates. Asymptotic normalities of the proposed estimators are established. Simulations are conducted to demonstrate finite sample behaviors of the proposed estimators, and real data examples are given to illustrate the value of the methodology.