We consider a robust version of the classical Wald test statistics for testing simple and composite null hypotheses for general parametric models. These test statistics are based on the minimum density power divergence estimators instead of the maximum likelihood estimators. An extensive study of their robustness properties is given though the influence functions as well as the chi-square inflation factors. It is theoretically established that the level and power of these robust tests are stable against outliers, whereas the classical Wald test breaks down. Some numerical examples confirm the validity of the theoretical results.
Bibliographical noteFunding Information:
This paper was supported by Ministerio de Economía y Competitividad of Spain , Grant MTM-2012-33740 .
© 2016 Elsevier Inc.
- Chi-square inflation factor
- Divergence measures
- Influence functions
- Minimum density power divergence estimators
- Wald-type test statistics