Revisiting I.J. Good's Bump Surgery Algorithm

• Activity Number: 132
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): David Scott*+
• Companies: Rice University
• Keywords: Bump hunting ; Testing Modes ; Kernel Density Estimation

Abstract

In 1980, I.J. Good and R.A. Gaskins introduced a novel nonparametric density estimation method based upon penalized likelihood. At the same time, they demonstrated how to modify the estimator to eliminate modes in order to assess the Bayesian odds in favor of a number of modes. The problem of assessing modes has been consider by numerous authors: Siverman (bootstrapping); Chaudhuri and Marron (SiZer, Scale space); Minnotte and Scott (mode tree); Minnotte (testing); Polonik and Mueller and Sawitzki (excess mass); Hartigan and Hartigan (DIP test); Fisher, Mammen, and Marron (testing); Escobar and West (Bayesian testing); Roeder (graphical); Minnotte, Marchette, and Wegman (mode forest); Holmstrom (Bayesian scale space). In this paper, we revisit Good's original idea by finding local polynomial patches to a kernel density estimator and computing the likelihood ratio in the manner of Good and Gaskins. This so-called patch algorithm is graphical in nature and is shown to behave empirically in a satisfactory manner.