IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v66y2014i5p961-981.html
   My bibliography  Save this article

Extensions of saddlepoint-based bootstrap inference

Author

Listed:
  • Robert Paige
  • A. Trindade
  • R. Wickramasinghe

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). 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. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • Robert Paige & A. Trindade & R. Wickramasinghe, 2014. "Extensions of saddlepoint-based bootstrap inference," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 961-981, October.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:5:p:961-981
    DOI: 10.1007/s10463-013-0434-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-013-0434-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-013-0434-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gómez, E. & Gómez-Villegas, M. A. & Marín, J. M., 2002. "Continuous Elliptical and Exponential Power Linear Dynamic Models," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 22-36, October.
    2. Mineo, Angelo & Ruggieri, Mariantonietta, 2005. "A Software Tool for the Exponential Power Distribution: The normalp Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i04).
    3. Gupta, Arjun K. & González-Farías, Graciela & Domínguez-Molina, J. Armando, 2004. "A multivariate skew normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 181-190, April.
    4. Wang, Tonghui & Li, Baokun & Gupta, Arjun K., 2009. "Distribution of quadratic forms under skew normal settings," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 533-545, March.
    5. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    6. Robert L. Paige & P. Harshini Fernando, 2008. "Robust Inference in Conditionally Linear Nonlinear Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(1), pages 158-168, March.
    7. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    8. Robert L. Paige & A. Alexandre Trindade & P. Harshini Fernando, 2009. "Saddlepoint‐Based Bootstrap Inference for Quadratic Estimating Equations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 98-111, March.
    9. Plosser, Charles I. & Schwert, G. William, 1977. "Estimation of a non-invertible moving average process : The case of overdifferencing," Journal of Econometrics, Elsevier, vol. 6(2), pages 199-224, September.
    10. Saralees Nadarajah, 2005. "A generalized normal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 685-694.
    11. Tanaka, Katsuto, 1990. "Testing for a Moving Average Unit Root," Econometric Theory, Cambridge University Press, vol. 6(4), pages 433-444, December.
    12. Davis, Richard A. & Dunsmuir, William T.M., 1996. "Maximum Likelihood Estimation for MA(1) Processes with a Root on or near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 12(1), pages 1-29, March.
    13. Huang, Wen-Jang & Chen, Yan-Hau, 2006. "Quadratic forms of multivariate skew normal-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 871-879, May.
    14. T. W. Anderson & Akimichi Takemura, 1986. "Why Do Noninvertible Estimated Moving Averages Occur?," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(4), pages 235-254, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vougas, Dimitrios V., 2008. "New exact ML estimation and inference for a Gaussian MA(1) process," Economics Letters, Elsevier, vol. 99(1), pages 172-176, April.
    2. Ye, Rendao & Wang, Tonghui & Gupta, Arjun K., 2014. "Distribution of matrix quadratic forms under skew-normal settings," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 229-239.
    3. Consuelo Arellano & Sastry G. Pantula, 1995. "Testing For Trend Stationarity Versus Difference Stationarity," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(2), pages 147-164, March.
    4. Sharon Lee & Geoffrey McLachlan, 2013. "On mixtures of skew normal and skew $$t$$ -distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(3), pages 241-266, September.
    5. Wang, Tonghui & Li, Baokun & Gupta, Arjun K., 2009. "Distribution of quadratic forms under skew normal settings," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 533-545, March.
    6. Huang, Wen-Jang & Chen, Yan-Hau, 2007. "Generalized skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1137-1147, June.
    7. Kim, Hyoung-Moon & Ryu, Duchwan & Mallick, Bani K. & Genton, Marc G., 2014. "Mixtures of skewed Kalman filters," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 228-251.
    8. Sharon Lee & Geoffrey McLachlan, 2013. "Model-based clustering and classification with non-normal mixture distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 427-454, November.
    9. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    10. Mauro Bernardi & Roy Cerqueti & Arsen Palestini, 2020. "The Skew Normal multivariate risk measurement framework," Computational Management Science, Springer, vol. 17(1), pages 105-119, January.
    11. Panagiotelis, Anastasios & Smith, Michael, 2010. "Bayesian skew selection for multivariate models," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1824-1839, July.
    12. Ismael Sanchez & Daniel Pena, 2001. "Properties of Predictors in Overdifferenced Nearly Nonstationary Autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(1), pages 45-66, January.
    13. Reinaldo B. Arellano-Valle & Marc G. Genton, 2010. "Multivariate extended skew-t distributions and related families," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 201-234.
    14. Yabe, Ryota, 2017. "Asymptotic distribution of the conditional-sum-of-squares estimator under moderate deviation from a unit root in MA(1)," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 220-226.
    15. M. Teimourian & T. Baghfalaki & M. Ganjali & D. Berridge, 2015. "Joint modeling of mixed skewed continuous and ordinal longitudinal responses: a Bayesian approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(10), pages 2233-2256, October.
    16. Fang, B.Q., 2006. "Sample mean, covariance and T2 statistic of the skew elliptical model," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1675-1690, August.
    17. Azzalini, Adelchi & Browne, Ryan P. & Genton, Marc G. & McNicholas, Paul D., 2016. "On nomenclature for, and the relative merits of, two formulations of skew distributions," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 201-206.
    18. Sladana Babic & Laetitia Gelbgras & Marc Hallin & Christophe Ley, 2019. "Optimal tests for elliptical symmetry: specified and unspecified location," Working Papers ECARES 2019-26, ULB -- Universite Libre de Bruxelles.
    19. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2007. "Model comparison of coordinate-free multivariate skewed distributions with an application to stochastic frontiers," Journal of Econometrics, Elsevier, vol. 137(2), pages 641-673, April.
    20. Reinaldo B. Arellano-Valle, 2010. "On the information matrix of the multivariate skew-t model," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 371-386.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:aistmt:v:66:y:2014:i:5:p:961-981. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.