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

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.