A Laplace Approximation to the Moments of a Ratio of Quadratic Forms

Offer Lieberman

No 267630, Department of Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: The Laplace method for integrals approximating is applied to give a general approximation for the kth moment of a ratio of quadratic forms in random variables. The technique utilizes the existence of a dominating peak at the boundary point on the range of integration. As closed form and tractable formulae do not exist in general, this simple approximation, which only entails basic algebraic operations, has evident practical appeal. We exploit the approximation to provide an approximate mean-bias function for the least squares estimator of the coefficient of the lag dependent variable in a first order stochastic difference equation.

Keywords: Research; Methods/Statistical; Methods (search for similar items in EconPapers)
Pages: 21
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Persistent link: https://EconPapers.repec.org/RePEc:ags:monebs:267630

DOI: 10.22004/ag.econ.267630

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