Analysis of Nonparametric Density Functionals Estimation (ANDFE): One-Way Layout

• Activity Number: 238
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Su Chen*+ and Ibrahim Ahmad
• Companies: University of Memphis and Oklahoma State University
• Keywords: ANOVA ; Kernel density estimation ; Location and scale parameters ; Kernel functionals estimation

Abstract

A novel nonparametric method of detecting differences among populations, namely "Analysis of Nonparametric Density Functionals Estimation (ANDFE)" is introduced and studied. ANDFE is nonparametric in the sense that no distributional format assumed and the testing pertain to locations and scales of unknown distributions. The ANDFE for locations (ANDFEL) parallels one-way ANOVA and Kruskal-Wallis (KW) test. In contrast to the rank-transformed nonparametric approach, such as KW, ANDFEL uses the measurement responses along with the highly recognized 'kernel density estimation' to estimate the locations and then construct the test. Under the stated hypothesis, the proposed F statistic is asymptotically F-distributed. Like ANOVA, ANDFEL test assumes homogeneous scales. Hence, ANDFE for scales (ANDFES), a nonparametric analog of Bartlett test is proposed as well. We conduct simulation studies and a real data example to illustrate our tests and conclude that our method is very powerful, particularly for heavy-tailed distributions.