Change-plane regression

Music City Center 

Change-point regression is linear regression where the regression coefficients change depending on whether another covariate is above or below an unknown threshold. Change-plane regression is a generalization of this where the regression cofficents change depending on whether another vector of covariates is above or below an unknown hyperplane. Since the residual error in this setting is assumed to be mean zero with finite variance, but is otherwise unspecified, this model is semiparametric. In this presentation, we derive for the first time the limiting distribution of the unknown parameters, under least-squares estimation, and when some of the covariates are allowed to be discrete. The limiting distribution is new and has not been previously characterized. In addition to theoretical results, we also present simulation studies and an illustrative data analysis of AIDS data for precision medicine.

Change-plane

Weak convergence