Applications of asymptotic inference in segmented line regression

Abstract

This paper studies asymptotic properties of the estimators of the regression coefficients in segmented line regression, focusing on the multi-phase regression model with the continuity constraint at the unknown change-points. We first review the asymptotic distributions of the least squares estimators of the regression coefficients and discuss why the standard error estimates of the estimators derived under the assumption of known change-points do not serve as good estimates although the change-point estimators are consistent. Then, we provide some details on the asymptotic distributions of the estimated regression coefficients in three extended cases: (i) the model with heteroscedastic errors, (ii) the model with abrupt jumps either at known or unknown jump points, in addition to continuous changes, and (iii) the fit made under the constraint on the minimum size of the estimated slope changes. Empirical properties of the standard error estimates of the estimated regression coefficients are studied via simulations.

Keywords:

• Multi-phase regression
• asymptotic distribution
• change-point