A new test for high‐dimensional regression coefficients in partially linear models

Abstract

Partially linear regression models are semiparametric models that contain both linear and nonlinear components. They are extensively used in many scientific fields for their flexibility and convenient interpretability. In such analyses, testing the significance of the regression coefficients in the linear component is typically a key focus. Under the high‐dimensional setting, i.e., “large p, small n,” the conventional F‐test strategy does not apply because the coefficients need to be estimated through regularization techniques. In this article, we develop a new test using a U‐statistic of order two, relying on a pseudo‐estimate of the nonlinear component from the classical kernel method. Using the martingale central limit theorem, we prove the asymptotic normality of the proposed test statistic under some regularity conditions. We further demonstrate our proposed test's finite‐sample performance by simulation studies and by analyzing some breast cancer gene expression data.

Application of LADMM and As-LADMM for a High-Dimensional Partially Linear Model

“…With the development of information and intelligence in the era of big data, the analysis of high-dimensional data has become an important research topic [1,2]. The relationships between variables of high-dimensional data are diverse and complex with the partially linear model being one of the most important relationships among them [3,4], and some research results have been achieved [5].…”