Lucent Technologies - Bell Laboratories
In the last decade a considerable body of literature on multivariate spline spaces has been amassed by approximation theorists, numerical analysts and computer scientists. Through this talk I hope to demonstrate the practicality of these tools for statistical applications. I will approach each application by constructing estimates that are bivariate splines defined over arbitrary triangulations. The triangulations themselves are constructed adatively, using techniques based on the stepwise addition and deletion of basis functions.
This is joint work with Charles Kooperberg and Sylvain Sardy.