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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Veröffentlicht in:Annals of the Institute of Statistical Mathematics Jg. 66; H. 5; S. 961 - 981
Hauptverfasser: Paige, Robert L., Trindade, A. Alexandre, Wickramasinghe, R. Indika P.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Tokyo Springer Japan 01.10.2014
Springer Nature B.V
Schlagworte:
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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Zusammenfassung: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.
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ISSN:0020-3157
1572-9052
DOI:10.1007/s10463-013-0434-9