Confidence Intervals for High-Dimensional Network-Auxiliary Expectile Regression Models

In this paper, we develop a statistical inference procedure by constructing confidence intervals and providing (Formula presented.) -values for parameters in a high-dimensional expectile regression model incorporating graph structures, where the dimensionality grows with sample size. We propose a graph-constrained desparsified LASSO (GCDL) estimator, which effectively reduce the impact of strong correlations among predictors. Compared to the conventional desparsified LASSO that ignores network information, GCDL improves computational efficiency and estimation accuracy. Theoretical analysis further shows that the GCDL estimator is asymptotically normal under mild regularity conditions. To assess its finite-sample performance, we conduct simulation studies under both homoscedastic and heteroscedastic scenarios. An application to a human liver cohort dataset further illustrates the practical utility of the method.