Thursday, September 21, 2000, 4:00 - 5:00 p.m.

**
at CICSR 208, 2366 Main Mall, UBC
**

**SPEAKER**: Professor Peter J. Rousseeuw

**TITLE**: An Introduction to Regression Depth

**ABSTRACT**:
In this talk we introduce a notion of depth in the regression
setting. It provides the rank of any line (plane), rather than ranks of
observations or residuals. In simple regression we can compute the depth of
any line by an $O(n \log n)$ algorithm. For any bivariate data set $Z_n$ of
size $n$ there exists a line with depth at least $n/3$. The largest depth
in $Z_n$ can be used as a measure of linearity versus convexity. In both
simple and multiple regression we consider the deepest fit, which
generalizes the univariate median and is equivariant for monotone
transformations of the response. Throughout, the errors may be skewed and
non-identically distributed (e.g. heteroskedastic). We also construct
depth-based regression quantiles. They estimate the quantiles of y given x,
as do the $L^1$-based regression quantiles, but can withstand the effect of
leverage points. Using the concept of regression depth, we obtain some new
results of discrete geometry.