Bilinear form test statistics for extremum estimation

TL;DR

This paper introduces bilinear form-based test statistics for extremum estimation, especially for nonlinear hypotheses, demonstrating their asymptotic chi-square distribution and good finite-sample performance.

Contribution

It proposes a new class of test statistics based on bilinear forms for extremum estimation, extending hypothesis testing methods.

Findings

Test statistic converges to chi-square distribution asymptotically.

Monte Carlo simulations show good finite-sample performance.

Applicable to nonlinear hypothesis testing in extremum estimation.

Abstract

This paper develops a set of test statistics based on bilinear forms in the context of the extremum estimation framework with particular interest in nonlinear hypothesis. We show that the proposed statistic converges to a conventional chi-square limit. A Monte Carlo experiment suggests that the test statistic works well in finite samples.