Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment ...

Let (Xi, ℱi)i≥1 be a sequence of martingale differences. Set Sn=Σi=1nXi and Sn=Σi=1n Xi2. We prove a Cramér type moderate deviation expansion for PSn/Sn≥x as n + ∞. Our results partly extend the ...

Dr. James McCaffrey of Microsoft Research uses a full code sample and screenshots to show how to programmatically normalize numeric data for use in a machine learning system such as a deep neural ...