My current research focuses on three distinct but interrelated topics.

1. High-Dimensional Inference: My research in this area is centered on developing parametric and nonparametric methods for analyzing high-dimensional data, especially for comparison of treatments or groups. High dimensional refers to both the sample size and dimension being large without any restriction on the rate of growth between the two. Recent high-dimensional methods make strong assumptions about the dependence between the variables, which may not be satisfied, for example, in elliptically contoured models or other dependence models. Our high-dimensional approach focuses on asymptotic methods that are applicable under weaker dependence conditions. The weaker conditions, among other things, make it possible to derive results for rank-based high-dimensional inference.

Representative Publications:

a) Harrar, S. W. and Hossler, J. Z. (2016), Methods for High-Dimensional Multivariate Repeated Measures Data under General Conditions. Statistics: A Journal of Theoretical and Applied Statistics 50(5), 1056--1074.

b) Harrar, S. W. and Kong X. (2016), High-Dimensional Repeated Measures Analysis with Unequal Covariance Matrices, Journal of Multivariate Analysis 145(1), 1--21.

2. Nonparametric Analysis of Clustered Data: Clustered data naturally arise when subjects or units of analysis are grouped in some way such that there is considerable amount of dependence within cluster. Methods for clustered data have been widely investigated from GEE, mixed model or Bayesian points of views. Not much attention has been given to the nonparametric analysis of clustered data. In this context, my research pertains to inference on the so-called nonparametric effects (Mann-Whitney effects) which quantity the tendency of one sample to be larger (smaller) than the other while accounting for the intra-cluster dependence. This approach, besides not making assumptions about data distributions not their moments, does not imply equal distribution under the null hypothesis. This phenomenon is referred to as the nonparametric Behrens-Fisher problem.

Representative Publications:

a) Roy, A., Harrar, S. W. and Konietschke, F., The nonparametric Behrens-Fisher Problem with Dependent Replicates.

b) Feyasa, M. B., Harrar, S. W. and Wencheko, E., Nonparametric Procedures for Partially Paired Data in Two Groups, (submitted).

3. Inference under Diagnostic Misclassification: In clinical trials or other comparative studies, diagnostic or screening devices often determine the status of patients for having the condition or trait of interest. Treatment modalities are allocated to groups based on the results of the diagnostic (screening) devices. Typical statistical analysis makes the assumption that the devices are 100% accurate but often times, these devices are prone to errors of unknown rate. Needless to say, ignoring these errors leads to incorrect inference and optimistic sample size estimates. In our researches in this direction, we develop methods to estimate and account for diagnostic errors while concurrently make inference about treatment effects.

Representative Publications:

a) Harrar, S. W., Amatya, A. and Kalachev, L. (2016), Assessing Treatment Efficacy in the Presence of Diagnostic Errors, Statistics in Medicine 35(29), 5338--5355.