Robust M tests without consistent estimation of asymptotic covariance matrix
Resource
Journal of the American Statisitical Association, 101, 1264-1275
Journal
Journal of the American Statistical Association,
Journal Issue
101
Pages
1264-1275
Date Issued
2006-01
Author(s)
Abstract
We extend the KVB approach of Kiefer, Vogelsang, and Bunzel (2000) to constructing robust M tests without consistent estimation of the asymptotic covariance matrix. We demonstrate that, when model parameters have to be estimated, the normalizing matrix computed using a full-sample estimator is able to eliminate the nuisance parameters when there is no estimation effect but not otherwise. To circumvent the problem of estimation effect, we propose using recursive estimators to compute the normalizing matrix and show that the resulting M test is asymptotically pivotal. This M test is, thus, robust not only to heteroscedasticity and serial correlations of unknown form but also to the presence of an estimation effect. As examples, we consider robust tests for serial correlations and robust information matrix tests. The former tests extend that of Lobato (2001) and are applicable to model residuals. For testing higher-order moments, we find that the latter tests are also robust when a lower-order moment is misspecified. Our simulations confirm that the proposed M tests are properly sized and have power advantage when other tests are computed based on inappropriate user-chosen parameters.
Type
journal article