Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics

Jean-Marie Dufour ()

Cahiers de recherche from Centre interuniversitaire de recherche en économie quantitative, CIREQ

Abstract: The technique of Monte Carlo (MC) tests [Dwass (1957), Barnard (1963)] provides an attractive method of building exact tests from statistics whose finite sample distribution is intractable but can be simulated (provided it does not involve nuisance parameters). We extend this method in two ways: first, by allowing for MC tests based on exchangeable possibly discrete test statistics; second, by generalizing the method to statistics whose null distributions involve nuisance parameters (maximized MC tests, MMC). Simplified asymptotically justified versions of the MMC method are also proposed and it is shown that they provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics (e.g., unit root asymptotics). Parametric bootstrap tests may be interpreted as a simplified version of the MMC method (without the general validity properties of the latter).

Keywords: Monte Carlo test; maximized monte Carlo test; finite sample test; exact test; nuisance parameter; bounds; bootstrap; parametric bootstrap; simulated annealing; asymptotics; nonstandard asymptotic distribution (search for similar items in EconPapers)
JEL-codes: C12 C15 C2 C22 C52 (search for similar items in EconPapers)
Pages: 45 pages
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Journal Article: Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics (2006)
Working Paper: Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and non-standard asymptotics (2005)
Working Paper: Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics (2005)
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