Admissible invariant similar tests for instrumental variables regression. (English) Zbl 1278.62029
Summary: This paper studies a model widely used in the weak instruments literature and establishes admissibility of the weighted average power likelihood ratio tests recently derived by D. W. K. Andrews et al. [Optimal invariant similar tests for instrumental variables regression. NBER Technical Working Paper 299 (2004), http://www.nber.org/papers/t0299]. The class of tests covered by this admissibility result contains the Anderson-Rubin test [T. W. Anderson and H. Rubin, Ann. Math. Stat. 20, 46–63 (1949; Zbl 0033.08002)]. Thus, there is no conventional statistical sense in which the Anderson-Rubin test “wastes degrees of freedom”. In addition, it is shown that the test proposed by M. J. Moreira [Econometrica 71, No. 4, 1027–1048 (2003; Zbl 1151.62367)] belongs to the closure of (i.e., can be interpreted as a limiting case of) the class of tests covered by our admissibility result.
MSC:
| 62F03 | Parametric hypothesis testing |
| 62C15 | Admissibility in statistical decision theory |
| 62H15 | Hypothesis testing in multivariate analysis |
References:
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