Detection and Estimation of Jumps in Regression Curves and Surfaces

Professor Anirban DasGupta

Wednesday, February 11, 2009
03:30 PM in REC 226

Abstract

Parametric linear regression assumes a finitely parametrized regression 
function, linear in the parameters. Traditional nonparametric regression 
assumes a smooth regression function, typically with derivative 
constraints. Discontinuous regression refers to regression functions
that have simultaneously a continuous part, and a finite number of 
possible jumps at unknown jump points. There are important extensions to 
two dimensions, where a regression surface is continuous except on a 
number of jump location curves JLCs).

The purpose of these talks is to introduce a family of methods to 
estimate the jump points and magnitudes, and the continuous part of a 
discontinuous regression function, study asymptotics, and point to 
applications, which are numerous. The methods include kernel smoothing, 
smoothing with local polynomials, spline smoothing, and also wavelets. 
There is also some decision theory literature. We find the area to be 
extremely interesting, although a substantial and powerful body of work
is already in place We plan to take most of the material from the 
following references:

Canny (1986), Chu et al. (1998), Eubank and Speckman (1994), Gijbels et 
al. (1999), Hall and Raimondo (1998), Hall and Rau (2000), Haralick  
(1984), Korostelev and Tsybakov (1993), Muller (1992), Muller and Song 
(1994), Qiu (2005), Qiu and Yandell (1997), Wang (1995).