Partial Martingale Difference Correlation

• Activity Number: 664
• Type: Contributed
• Date/Time: Thursday, August 4, 2016 : 8:30 AM to 10:30 AM
• Sponsor: IMS
• Author(s): Trevor Park* and Xiaofeng Shao and SHUN YAO
• Companies: University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign
• Keywords: distance correlation ; nonlinear dependence ; partial correlation ; variable selection

Abstract

We introduce partial martingale difference correlation (pMDC), a scalar-valued measure of conditional mean dependence of Y given X, adjusting for the nonlinear dependence on Z, where X, Y, and Z are random vectors of arbitrary dimensions. This measure is like partial distance correlation (Székely and Rizzo, 2014), but with express focus on the conditional mean of Y, making it potentially more relevant to regression. It also extends martingale difference correlation (Shao and Zhang, 2014) in the same way that partial distance correlation extends distance correlation (Székely, Rizzo, and Bakirov, 2007). We present numerical comparisons in the context of variable selection and dependence testing.