Extensions of saddlepoint-based bootstrap inference

We propose two substantive extensions to the saddlepoint-based bootstrap (SPBB) methodology, whereby inference in parametric models is made through a monotone quadratic estimating equation (QEE). These are motivated through the first-order moving average model, where SPBB application is complicated...

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Vydáno v:	Annals of the Institute of Statistical Mathematics Ročník 66; číslo 5; s. 961 - 981
Hlavní autoři:	Paige, Robert L., Trindade, A. Alexandre, Wickramasinghe, R. Indika P.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Tokyo Springer Japan 01.10.2014 Springer Nature B.V
Témata:	Approximation Bootstrap method Density Economics Estimators Finance Generalized method of moments Inference Insurance Laplace transforms Management Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Monte Carlo simulation Polynomials Random variables Roots Statistics Statistics for Business Studies Time series Mixed distribution Elliptically contoured distribution MA Exponential power distribution Estimating equation Moving average model Saddlepoint approximation
ISSN:	0020-3157, 1572-9052
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Popis
Shrnutí:	We propose two substantive extensions to the saddlepoint-based bootstrap (SPBB) methodology, whereby inference in parametric models is made through a monotone quadratic estimating equation (QEE). These are motivated through the first-order moving average model, where SPBB application is complicated by the fact that the usual estimators, method of moments (MOME), least squares, and maximum likelihood (MLE), all have mixed distributions and tend to be roots of high-order polynomials that violate the monotonicity requirement. A unifying perspective is provided by demonstrating that these estimators can all be cast as roots of appropriate QEEs. The first extension consists of two double saddlepoint-based Monte Carlo algorithms for approximating the Jacobian term appearing in the approximated density function of estimators derived from a non-monotone QEE. The second extension considers inference under QEEs from exponential power families. The methods are demonstrated for the MLE under a Gaussian distribution, and the MOME under a joint Laplace distribution for the process.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23
ISSN:	0020-3157 1572-9052
DOI:	10.1007/s10463-013-0434-9