Simulation-based assessment is a popular and frequently necessary approach to evaluation of statistical procedures. Sometimes overlooked is the ability to take advantage of underlying mathematical relations and we focus on this aspect. We show how to take advantage of large-sample theory when conducting a simulation using the analysis of genomic data as a motivating example. The approach uses convergence results to provide an approximation to smaller-sample results, results that are available only by simulation. We consider evaluating and comparing a variety of ranking-based methods for identifying the most highly associated SNPs in a genome-wide association study, derive integral equation representations of the pre-posterior distribution of percentiles produced by three ranking methods, and provide examples comparing performance. These results are of interest in their own right and set the framework for a more extensive set of comparisons.
Numerical Analysis and Computation
Louis, Thomas A. and Ruczinski, Ingo, "EFFICIENT EVALUATION OF RANKING PROCEDURES WHEN THE NUMBER OF UNITS IS LARGE WITH APPLICATION TO SNP IDENTIFICATION" (February 2009). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 182.