Bounds for inference with nuisance parameters present only under the alternative

Paper number: 00/13

Paper date: July 2000

Year: 2000

Paper Category: Working Paper

Authors

Filippo Altissimo and Valentina Corradi

Abstract

In hypothesis testing with nuisance parameters present only under the alternative two issues typically arise: (i) critical values are data dependent and so cannot be tabulated; (ii) we need to choose a functional over the nuisance parameter space. We address the first issue by providing easily computable bounds for the case of dependent and heterogeneous observations. We tackle the second issue by suggesting a weighted average statistic with weights given by the (quasi) likelihood over the nuisance parameter space. The small sample behavior of our procedure is analyzed via Monte Carlo simulations; we consider conditional moment tests and tests for nonlinearities in the SETAR model. For samples of 200-400 observations, the behaviour of the suggested weighted average statistic is rther satisfactory. An empirical illustration to the modeling of US male unemployment is provided.

Bounds for inference with nuisance parameters present only under the alternative Bounds for inference with nuisance parameters present only under the alternative