Boundary crossing Random Walks, clinical trials and multinomial sequential estimation

TL;DR

This paper establishes a sufficient condition for the uniqueness of multinomial sequential unbiased estimators, applies them to boundary-crossing random walks, and demonstrates their use in clinical trial parameter inference.

Contribution

It generalizes classical binomial results to multinomial cases and introduces unbiased estimators for boundary-crossing random walks with clinical trial applications.

Findings

Provided a new sufficient condition for estimator uniqueness.

Applied unbiased estimators to multidimensional boundary-crossing random walks.

Demonstrated clinical trial parameter inference using these estimators.

Abstract

A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or multinomial Random Walks which are observed until they reach a boundary. An application to clinical trials is presented.