Simple Robust Testing of Regression Hypotheses

• Published in: Econometrica Vol. 68; no. 3; pp. 695 - 714
• Main Authors: Kiefer, Nicholas M., Vogelsang, Timothy J., Bunzel, Helle
• Format: Journal Article
• Language: English
• Published: Oxford, UK and Boston, USA Blackwell Publishers Ltd 01-05-2000; Econometric Society; Blackwell; George Banta Pub. Co. for the Econometric Society; Blackwell Publishing Ltd
• Subjects: Confidence interval; Consistent estimators; Correlation; Critical values; Econometrics; Economic models; Economic theory; Estimation methods; Estimators; Exact sciences and technology; Gross domestic product; Heteroskedasticity; Hypotheses; Hypothesis testing; Inference; Least squares method; Linear inference, regression; Mathematical economics; Mathematics; Nonparametric inference; Notes and Comments; Parametric inference; Probabilities; Probability and statistics; Regression analysis; Sciences and techniques of general use; Statistics; Studies; Testing; Time series; Statistical regression; Hypothesis test; Density estimation; Empirical process; Critical value; Sample size; Test robustness; Asymptotic behavior; Sampling; Stochastic process
• ISSN: 0012-9682; 1468-0262
• DOI: 10.1111/1468-0262.00128

The problem of hypothesis testing in models with errors that have serial correlation for heteroscedasticity of unknown form is considered. An alternative method of constructing robust test statistics is proposed. A nonsingular data dependent stochastic transformation to the ordinary least squares estimates is applied. The asymptotic distribution of the transformed estimates does not depend on nuisance parameters. Then, test statistics that are asymptotically invariant to nuisance parameters are constructed. The resulting test statistics have nonstandard asymptotic distributions that only depend on the number of restrictions being tested, and critical values are easy to simulate using standard techniques.