Research

St. Petersburg Mathematics Seminar
(Leader: )

Thursday, November 14, 2024

Title: Asymptotic Distribution-Free Goodness-of-fit Test through Khmaladze Martingale Transformation
Speaker: Jiwoong Kim
Time: 4:00pm–5:30pm
Place: DAV 265

Abstract

Khmaladze martingale transformation provides an asymptotically-distribution-free method for a goodness-of-fit test. With its usage not being restricted to testing for normality, it can also be selected to test for distributions of extreme evetns such as Cauchy and Gumbel distributions. Despite its merits, the Khmaladze martingale transformation, however, could not have enjoyed deserved celebrity since it is computationally expensive; it entails the complex and time-consuming computations, including optimization, integration of a fractional function, matrix inversion, etc. To overcome these computational challenges, this paper proposes a fast algorithm which provides a solution to the Khmaladze martingale transformation method. To that end, the proposed algorithm is equipped with a novel strategy, named integration-in-advance, which rigorously exploits the structure of the Khmaladze martingale transformation.