Local optimization-based statistical inference

TL;DR

This paper proposes a local optimization-based method for hypothesis testing and confidence interval construction, extending bootstrap techniques with algorithms like neighborhood bootstrap, effective even in complex theoretical scenarios.

Contribution

It introduces a novel local optimization approach that extends bootstrap methods for more flexible and effective statistical inference.

Findings

Asymptotically valid tests and intervals are achieved.

Effective in complex scenarios where theoretical analysis is challenging.

Algorithms like neighborhood bootstrap demonstrate practical utility.

Abstract

This paper introduces a local optimization-based approach to test statistical hypotheses and to construct confidence intervals. This approach can be viewed as an extension of bootstrap, and yields asymptotically valid tests and confidence intervals as long as there exist consistent estimators of unknown parameters. We present simple algorithms including a neighborhood bootstrap method to implement the approach. Several examples in which theoretical analysis is not easy are presented to show the effectiveness of the proposed approach.