Likelihood-based Inference for Regular Functions with Fractional Polynomial Approximations

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Journal Article
Journal of Econometrics, 2014, 183 (1), pp. 22 - 30
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The paper demonstrates limitations in previous work using Müntz-Szatz polynomial approximations for regular functions. It introduces an alternative set of fractional polynomial approximations not subject to these limitations. Using Weierstrass approximation theory it shows that the set of fractional polynomial approximations is dense on a Sobolev space of functions on a com-pact set. Imposing regularity conditions directly on the fractional polynomi-als produces pseudo-true approximations that converge rapidly to productions functions having no exact representation as fractional polynomials. A small Monte Carlo study recovers this convergence in Ânite sample, and the results are promising for future development of an adequate sampling-theoretic distribution theory.
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