Institut für Statistik

Vortragsankündigung

Prof. Dr. Nancy E. Heckman

Quantifying Similarity of Shape of Regression Functions

Abstract:

Does a regression function follow a specified shape?
Are two regression functions the same shape?
How can regression functions be grouped, based on shape?
These questions can occur when investigating monotonicity or when studying variation in families of curves. To begin to address these questions one must quantify similarity of shape between two curves. The rank correlation coefficient between two functions is just such a measure. This correlation is a generalisation of the rank correlation between two finite sets of numbers and is equal to one if and only if the two functions have the same shape (in a certain sense). A sample rank correlation based on smoothed estimates of the regression functions consistently estimates the true correlation. This sample rank correlation is applied to weather data and astronomical data to find clusters of similar weather patterns and light emission patterns, respectively.

Most of the work appears in:
Heckman, N. and Zamar, R. (2000). "Comparing the shapes of regression functions", Biometrika 87: 135-144.
This is available on the web:
www.stat.ubc.ca/people/nancy/ --> Publications