Local-Moment Polynomial-Smoothed Histograms with Application to Massive and Pre-Binned Datasets

• Activity Number: 543
• Type: Contributed
• Date/Time: Thursday, August 2, 2007 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Galen Papkov*+ and David W. Scott
• Companies: Rice University and Rice University
• Keywords: Polynomial histogram ; Nonparametric density estimation ; smoothing ; massive data sets ; binned data ; massive data sets ; binned data

Abstract

This paper suggests some logical and preferential modifications to Scott and Sagae's (1997) local moment method, the smoothed polynomial histogram (SPH), which uses a basis of truncated power functions (TPF) along with a roughness penalty to conduct nonparametric density estimation. Alternative tools presented in this paper include the addition of a weight matrix to be more faithful to information obtained from high-density bins, the use of B-splines which are more numerically stable than TPF, implementation of P-splines with a difference penalty which is simpler to code compared to a roughness penalty and increases computational efficiency, and quadratic programming to compensate for occasional negativity within the estimated densities. Finally, a procedure for extrapolating a smoothed polynomial histogram to higher dimensions via tensor products of B-splines is introduced.