A Neighborhood Hypothesis Test for a High-Dimensional Mean When the Neighborhood Is Defined in Terms of the Total Population Variance with an Application to Model Validation

• Activity Number: 57 - Nonparametric Modeling I
• Type: Contributed
• Date/Time: Sunday, August 8, 2021 : 3:30 PM to 5:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Dhanamalee Bandara* and Leif Ellingson and Souparno Ghosh
• Companies: University of Wisconsin Green Bay and Texas Tech University and University of Nebraska Lincoln
• Keywords: Functional data; neighborhood hypothesis test; Hotelling T-squared statistic; Pharmacogenomic database; Fréchet variation; homogeneity

Abstract

Traditional multivariate tests for means often fail in high dimensions or with functional data due in part to the rank deficiency of the sample covariance matrix. Accommodations to T-squared-style statistics to accommodate this deficiency are often only applicable with prohibitively large sample sizes. An alternative solution is to replace the classical null hypothesis with a neighborhood hypothesis to test for approximate equality. The existing methods for this require the size of the neighborhood to be specified a priori with respect to a distance measure which may be difficult to interpret practically. Additionally, since sample spaces are not compact for many applications, it can be difficult to determine an appropriate upper bound for the radius of the neighborhood. Hence, we propose a novel modified neighborhood testing procedure that defines a neighborhood as a proportion of the total amount of variation present in the population under study. Here, we present a novel test statistic and describe its properties through asymptotic results and simulation studies. Finally, we apply this framework to address a problem arising in the field of precision medicine.