Testing (Infinitely) Many Zero Restrictions
Abstract
This paper proposes a maxtest 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 subparameters 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 pvalue computation without directly requiring the maxstatistic's limit distribution. A simulation experiment shows the maxtest dominates a conventional bootstrapped test.
 Publication:

arXiv eprints
 Pub Date:
 November 2020
 arXiv:
 arXiv:2011.01983
 Bibcode:
 2020arXiv201101983H
 Keywords:

 Mathematics  Statistics Theory;
 62G10;
 62M99;
 62F35