Detection and Estimation of Jumps in Regression Curves
and Surfaces

Professor Anirban DasGupta

Abstract

In the second lecture of the series, we will first complete
the one dimensional case with a set of concrete results on
the consistency and asymptotic distribution of estimates of the jump 
point and the jump magnitude, and discuss confidence intervals for them.
We then take the two dimensional case, where an image intensity
function has discontinuities along a jump location curve(JLC).
The main problems are to estimate the JLC and a suitable
function that measures the jump.

Only asymptotics are feasible in these problems, although one can also 
do some asymptotic decision theory. In particular, some asymptotic 
decision theory in a simple in-or-out image processing model will be 
presented, although it may have to be postponed till the third lecture.