A New Construction of Triogram Model

• Activity Number: 662
• Type: Topic Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Huijun Pan* and Jianhua Huang+
• Companies: Texas A&M University and Texas A&M University
• Keywords: nonparametric function estimation ; 2-d splines ; regularization

Abstract

We consider smoothing data over domains on a plane with complex irregular boundaries or interior holes. The success of data smoothing using splines in 1-d provides a strong motivation to construct flexible 2-d splines for this problem. Hansen, Kooperberg and Sardy introduced a family of continuous, piecewise linear functions defined over triangulations of the plane. These triograms enjoy a natural affine equivalence property that offers advantages over competing tensor product splines. However, such triograms do not enforce smoothness in the estimated surface and thus they work well for functions with ridges but not smooth functions. In this talk, we present a new class of triograms that are smooth piecewise cubic splines with local support. We illustrate the application of this new 2-d spline class using an example of smoothing a spatial data set.