Hypothesis Testing for Heteroscedastic Functional Data

• Activity Number: 354
• Type: Topic Contributed
• Date/Time: Wednesday, August 10, 2005 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Haiyan Wang*+ and Akritas G. Michael
• Companies: Kansas State University and The Pennsylvania State University
• Keywords: asymptotic theory of quadratic forms ; functional data ; nonparametric hypotheses ; projection method ; rank tests ; nonclassical setting

Abstract

Models for analyzing data involving repeated measurements within a subject or stratum include ordinary and generalized linear and nonlinear mixed-effects models in addition to the fully nonparametric marginal model. These approaches are suitable when the number of within-stratum measurements is relatively small. Time series models, smoothing spline models, and varying coefficient models also can be used for functional or curve data where the number of within stratum measurements is large. However, these impose modeling assumptions that restrict full generality. Here, we consider the fully nonparametric marginal model with unspecified covariance structure in the context of functional data and present procedures for evaluating the effect of several crossed factors on the curve and their interactions with time. The asymptotics, which rely on the large number of measurements per curve and not on large group sizes, hold under the general assumption of $\alpha$-mixing and do not require the measurements to be continuous or homoscedastic. However, such asymptotics require strong moment conditions. A competing set of rank procedures is developed that require no moment conditions.