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

Author

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  • José M.R. Murteira

    (CeBER, Faculdade de Economia da Universidade de Coimbra, and CEMAPRE)

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.

Suggested Citation

  • José M.R. Murteira, 2018. "Copula-based Tests for Nonclassical Measurement Error – The Case of Fractional Random Variables," CeBER Working Papers 2018-13, Centre for Business and Economics Research (CeBER), University of Coimbra.
    • Handle: RePEc:gmf:papers:2018-13
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    File URL: https://www.uc.pt/en/uid/ceber/WorkingPapers/wp/wp_2018/wpdecimoterceiro
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Copula; Fractional variable; Maximum likelihood; Measurement error; Probability integral transform; Score test.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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