Testing (Infinitely) Many Zero Restrictions

TL;DR

This paper introduces a max-test for evaluating infinitely many zero restrictions in extremum estimation, leveraging a novel estimator approach that improves accuracy, reduces complexity, and enhances test power.

Contribution

It proposes a new max-test methodology for infinite zero restrictions that avoids sparsity assumptions and improves estimation accuracy in nonlinear regression models.

Findings

Max-test outperforms conventional bootstrap tests in simulations.

Estimation method achieves sharper size and greater power.

Uses weighted estimators for better control of dispersion.

Abstract

This paper proposes a max-test for testing (possibly infinitely) many zero parameter restrictions in an extremum estimation framework. The test statistic is formed by estimating key parameters one at a time based on many empirical loss functions that map from a low dimension parameter space, and choosing the largest in absolute value from these individually estimated parameters. The parsimoniously parametrized loss identify whether the original parameter of interest is or is not zero. Estimating fixed low dimension sub-parameters ensures greater estimator accuracy, does not require a sparsity assumption, and using only the largest in a sequence of weighted estimators reduces test statistic complexity and therefore estimation error, ensuring sharper size and greater power in practice. Weights allow for standardization in order to control for estimator dispersion. In a nonlinear parametric regression framework we provide a parametric wild bootstrap for p-value computation without directly requiring the max-statistic's limit distribution. A simulation experiment shows the max-test dominates a conventional bootstrapped test.