Extensions of Saddlepoint-Based Bootstrap Inference with Application to the First-Order Moving Average Model

• Activity Number: 431
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Alexandre Trindade*+ and Robert Paige and R. Indika Wickramasinghe
• Companies: Texas Tech University and Department of Mathematics and Statistics, Missouri University of Science and Technology and Eastern New Mexico University
• Keywords: saddlepoint approximation ; estimating equation ; mixed distribution ; elliptically-contoured distribution ; exponential power distribution

Abstract

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) of which the estimator of interest is the unique root. SPBB application in an MA(1) is complicated by the fact that the usual estimators, method of moments (MOME), conditional least squares (CLSE), and maximumlikelihood (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 a double-saddlepoint based algorithm for computing an intractable conditional expectation for the Jacobian of the non-monotone QEE. An application to the MLE reveals the superiority of this approach in capturing the point masses that occur on the boundary of the parameter space. The second extension considers inference under QEEs from skew-normal and exponential power (EP) families. The method is shown to work well for the MA(1) under a joint Laplace distribution.