Nonparametric Estimation of a Change Point of a Regression Function

• Activity Number: 74
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xiyue Liao* and Mary Catherine Meyer
• Companies: and Colorado State University
• Keywords: jump-point ; inflection-point ; mode estimation ; convergence rates ; constrained regression

Abstract

We consider estimating a regression function f and a change-point m, where m is a jump-point, a mode, or an inflection point. Linear inequality constraints are used with spline regression functions to estimate m and f simultaneously using profile methods. For a given m, the maximum-likelihood estimate of f is found using constrained regression methods, then the set of possible change-points is searched to find the estimate that maximizes the likelihood. Convergence rates are obtained for each type of change-point estimator, and we show an oracle property, that the convergence rate of the regression function estimator is as if m were known. Parametrically modeled covariates are easily incorporated in the model. Simulations show that for small and moderate sample sizes, these methods compare well to existing methods.