A Simple Distribution-Free Algorithm for Generating Simulated High-Dimensional Correlated Data with an Autoregressive Structure

Abstract

A distribution-free method to generate high-dimensional sequences of dependent variables with an autoregressive structure is presented. The quantile or fractile correlation (i.e., the moment correlation of the quantiles) is used as measure of dependence among a set of contiguous variables. The proposed algorithm breaks the sequence in small parts and avoids having to define one large correlation matrix for the entire high-dimensional sequence of variables. Simulations based on proteomics data are presented. Results suggest that negligible or no loss of fractile correlation occurs by splitting the generation of a sequence into small parts.

Keywords:

• Distribution-free methods
• Fractile correlations
• High-dimensional data
• Simulation

Mathematics Subject Classification:

• 00A72
• 68U20
• 62P99
• 62H20
• 15A99

Acknowledgment

This publication was supported by Grant Number (U54 CA118948-01) from the National Cancer Institute.

Notes

¹Evaluated on Uniform(0,1) variables.

²Evaluated on variables generated under a Dagum distribution.

³Evaluated on variables generated under Dagum or Gamma distributions.