Aaron Heuser | Searcharxiv

arXiv2017

Asymptotic convergence in distribution of the area bounded by prevalence-weighted Kaplan-Meier curves using empirical process modeling

The Kaplan-Meier product-limit estimator is a simple and powerful tool in time to event analysis. An extension exists for populations stratified into cohorts where a population survival curve is generated by weighted averaging of cohort-level survival curves. For making population-level comparisons using this statistic, we analyze the statistics of the area between two such weighted survival curves. We derive the large sample behavior of this statistic based on an empirical process of product-limit estimators. This estimator was used by an interdisciplinary NIH-SSA team in the identification of medical conditions to prioritize for adjudication in disability benefits processing.

stat.ME↗

arXiv2012

Generalized self-intersection local time for a superprocess over a stochastic flow

This paper examines the existence of the self-intersection local time for a superprocess over a stochastic flow in dimensions $d\leq3$, which through constructive methods, results in a Tanaka-like representation. The superprocess over a stochastic flow is a superprocess with dependent spatial motion, and thus Dynkin's proof of existence, which requires multiplicity of the log-Laplace functional, no longer applies. Skoulakis and Adler's method of calculating moments is extended to higher moments, from which existence follows.

math.PR↗