Detecting Discontinuities in a Regression Curve

• Activity Number: 510 - New Developments in Time Series Analysis and Change Point Detection
• Type: Contributed
• Date/Time: Wednesday, August 2, 2017 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Cidambi Srinivasan* and Sisheng Liu and Richard Charnigo
• Companies: University of Kentucky and University of Kentucky and University of Kentucky
• Keywords: Curve estimation ; Discontinuities ; Deetction

Abstract

Detecting Discontinuities in a Regression Curve R. Charnigo, S. Liu, and C. Srinivasan Consider the familiar nonparametric regression with 1-dimensional response Y and covariate X in a compact interval. Suppose the mean curve mu(x) = E(Y | x) is known to have finitely many discontinuities at unknown locations. We present two methods for detecting the locations of the discontinuities and estimating the magnitudes of the jumps from n independent realizations of (Y,X). The first method is based on a process of increments of a local regression or kernel smooth estimator of mu(x). The second method is built on the empirical derivatives. We show the methods have asymptotically desirable properties of correct estimation of the locations and the jumps and compare them. Discontinuities or change points are common in applications and we briefly discuss implications of the results in nano-sciences.