Copula-based Tests for Nonclassical Measurement Error – The Case of Fractional Random Variables

José M.R. Murteira ()
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José M.R. Murteira: CeBER, Faculdade de Economia da Universidade de Coimbra, and CEMAPRE

No 2018-13, CeBER Working Papers from Centre for Business and Economics Research (CeBER), University of Coimbra

Abstract: This paper addresses measurement error (ME) of double bounded variables, of which fractional variables, defined on the interval [0,1], constitute a prominent example. The text discusses consequences of ME and suggests a specification test sensitive to ME of such variables. Given the latter’s bounded support, ME is not independent of the original error-free variate, a fact that invalidates classical ME assumptions as a framework for the test. This is circumvented with a score test of independence between the error-free variate and ME, under which the latter becomes degenerate at zero and their joint distribution, specified as a copula function, reduces to the original variable’s distribution. This procedure yields a specification test of the distribution of the error-free variable, valid under mild assumptions on the marginal distribution of ME and under departures from the specified copula. The test’s finite-sample behaviour is also evaluated through a set of simulation experiments.

Keywords: Copula; Fractional variable; Maximum likelihood; Measurement error; Probability integral transform; Score test. (search for similar items in EconPapers)
JEL-codes: C12 C25 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2018-12
New Economics Papers: this item is included in nep-ecm
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