Pairwise Difference Estimation of High Dimensional Partially Linear Model

TL;DR

This paper introduces a regularized pairwise difference method for estimating coefficients in high-dimensional partially linear models, demonstrating consistency, adaptive bandwidth, and applicability to brain imaging data.

Contribution

It develops a novel regularized pairwise difference estimator that is tuning-insensitive and effective in high dimensions, with theoretical guarantees and practical advantages.

Findings

Estimator achieves consistency and optimal convergence rates.

Bandwidth parameter adapts automatically to the model.

Method uncovers biological patterns in brain imaging data.

Abstract

This paper proposes a regularized pairwise difference approach for estimating the linear component coefficient in a partially linear model, with consistency and exact rates of convergence obtained in high dimensions under mild scaling requirements. Our analysis reveals interesting features such as (i) the bandwidth parameter automatically adapts to the model and is actually tuning-insensitive; and (ii) the procedure could even maintain fast rate of convergence for $\alpha$-H\"older class of $\alpha\leq1/2$. Simulation studies show the advantage of the proposed method, and application of our approach to a brain imaging data reveals some biological patterns which fail to be recovered using competing methods.