COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1015

"Optimal Tests When a Nuisance Parameter is Present Only Under the Alternative"

Donald W.K. Andrews and Werner Ploberger

April 1992

This paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null. The results of the paper are of interest, because the testing problem considered in non-standard and the classical asymptotic optimality results for the Wald, Lagrange multiplier (LM), and likelihood ratio (LR) tests do not apply. In the non-standard cases of main interest, new optimal tests are obtained and the LR test is not found to be an optimal test.

JE Classification: C12

Keywords: Asymptotics, changepoint, nonstandard testing problem