Efficient Tests under a Weak Convergence Assumption

43 Pages Posted: 15 Mar 2008 Last revised: 21 Jan 2009

See all articles by Ulrich K. Müller

Ulrich K. Müller

Princeton University - Department of Economics

Date Written: December 2008

Abstract

The paper studies the asymptotic efficiency and robustness of hypothesis tests when models of interest are defined in terms of a weak convergence property. The null and local alternatives induce different limiting distributions for a random element, and a test is considered robust if it controls asymptotic size for all data generating processes for which the random element has the null limiting distribution. Under weak regularity conditions, asymptotically robust and efficient tests are then simply given by efficient tests of the limiting problem - that is, with the limiting random element assumed observed - evaluated at sample analogues. These tests typically coincide with suitably robustified versions of optimal tests in canonical parametric versions of the model. This paper thus establishes an alternative and broader sense of asymptotic efficiency for many previously derived tests in econometrics, such as tests for unit roots, parameter stability tests and tests about regression coefficients under weak instruments.

Keywords: robustness, unit root test, semiparametric efficiency

JEL Classification: C12, C14

Suggested Citation

Müller, Ulrich K., Efficient Tests under a Weak Convergence Assumption (December 2008). Available at SSRN: https://ssrn.com/abstract=1105731 or http://dx.doi.org/10.2139/ssrn.1105731

Ulrich K. Müller (Contact Author)

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States
609-258-3216 (Phone)
609-258-4026 (Fax)

HOME PAGE: http://www.princeton.edu/~umueller

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