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

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.


Issue Date:
Jul 01 1994
Publication Type:
Working or Discussion Paper
Record Identifier:
http://ageconsearch.umn.edu/record/267630
Language:
English
Total Pages:
21
Series Statement:
Working Paper No. 13/94




 Record created 2018-02-01, last modified 2018-02-02

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