IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v114y2017icp75-87.html
   My bibliography  Save this article

On two-stage Monte Carlo tests of composite hypotheses

Author

Listed:
  • Baddeley, Adrian
  • Hardegen, Andrew
  • Lawrence, Thomas
  • Milne, Robin K.
  • Nair, Gopalan
  • Rakshit, Suman

Abstract

A major weakness of the classical Monte Carlo test is that it is biased when the null hypothesis is composite. This problem persists even when the number of simulations tends to infinity. A standard remedy is to perform a double bootstrap test involving two stages of Monte Carlo simulation: under suitable conditions, this test is asymptotically exact for any fixed significance level. However, the two-stage test is shown to perform poorly in some common applications: for a given number of simulations, the test with the smallest achievable significance level can be strongly biased. A ‘balanced’ version of the two-stage test is proposed, which is exact, for all achievable significance levels, when the null hypothesis is simple, and which performs well for composite null hypotheses.

Suggested Citation

  • Baddeley, Adrian & Hardegen, Andrew & Lawrence, Thomas & Milne, Robin K. & Nair, Gopalan & Rakshit, Suman, 2017. "On two-stage Monte Carlo tests of composite hypotheses," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 75-87.
    • Handle: RePEc:eee:csdana:v:114:y:2017:i:c:p:75-87
    DOI: 10.1016/j.csda.2017.04.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947317300762
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2017.04.003?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. Phipson Belinda & Smyth Gordon K, 2010. "Permutation P-values Should Never Be Zero: Calculating Exact P-values When Permutations Are Randomly Drawn," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-16, October.
    2. Hinkley, D. V., 1997. "Discussion of paper by H. Li & G.S. Maddala," Journal of Econometrics, Elsevier, vol. 80(2), pages 319-323, October.
    3. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
    4. Ute Hahn & Eva B. Vedel Jensen, 2016. "Hidden Second-order Stationary Spatial Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 455-475, June.
    5. Ute Hahn, 2012. "A Studentized Permutation Test for the Comparison of Spatial Point Patterns," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 754-764, June.
    6. Yongtao Guan, 2008. "A goodness-of-fit test for inhomogeneous spatial Poisson processes," Biometrika, Biometrika Trust, vol. 95(4), pages 831-845.
    7. Martin Bland, 2013. "Do Baseline P-Values Follow a Uniform Distribution in Randomised Trials?," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-5, October.
    8. Baddeley, Adrian & Turner, Rolf, 2005. "spatstat: An R Package for Analyzing Spatial Point Patterns," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i06).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Borrajo, M.I. & González-Manteiga, W. & Martínez-Miranda, M.D., 2024. "Goodness-of-fit test for point processes first-order intensity," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).

    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. Mari Myllymäki & Tomáš Mrkvička & Pavel Grabarnik & Henri Seijo & Ute Hahn, 2017. "Global envelope tests for spatial processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 381-404, March.
    2. Isabel Fuentes-Santos & Wenceslao González-Manteiga & Jorge Mateu, 2016. "Consistent Smooth Bootstrap Kernel Intensity Estimation for Inhomogeneous Spatial Poisson Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 416-435, June.
    3. Laura Anton-Sanchez & Pedro Larrañaga & Ruth Benavides-Piccione & Isabel Fernaud-Espinosa & Javier DeFelipe & Concha Bielza, 2017. "Three-dimensional spatial modeling of spines along dendritic networks in human cortical pyramidal neurons," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-14, June.
    4. Jonatan A. González & Bernardo M. Lagos-Álvarez & Jorge Mateu, 2021. "Two-way layout factorial experiments of spatial point pattern responses in mineral flotation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 1046-1075, December.
    5. Ute Hahn & Eva B. Vedel Jensen, 2016. "Hidden Second-order Stationary Spatial Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 455-475, June.
    6. Bernard, Jean-Thomas & Idoudi, Nadhem & Khalaf, Lynda & Yelou, Clement, 2007. "Finite sample multivariate structural change tests with application to energy demand models," Journal of Econometrics, Elsevier, vol. 141(2), pages 1219-1244, December.
    7. Takahashi, Makoto & Watanabe, Toshiaki & Omori, Yasuhiro, 2016. "Volatility and quantile forecasts by realized stochastic volatility models with generalized hyperbolic distribution," International Journal of Forecasting, Elsevier, vol. 32(2), pages 437-457.
    8. Arii, Ken & Caspersen, John P. & Jones, Trevor A. & Thomas, Sean C., 2008. "A selection harvesting algorithm for use in spatially explicit individual-based forest simulation models," Ecological Modelling, Elsevier, vol. 211(3), pages 251-266.
    9. Frank Davenport, 2017. "Estimating standard errors in spatial panel models with time varying spatial correlation," Papers in Regional Science, Wiley Blackwell, vol. 96, pages 155-177, March.
    10. Emma Iglesias & Jean Marie Dufour, 2004. "Finite Sample and Optimal Inference in Possibly Nonstationary ARCH Models with Gaussian and Heavy-Tailed Errors," Econometric Society 2004 North American Summer Meetings 161, Econometric Society.
    11. Leandro, Camila & Jay-Robert, Pierre & Mériguet, Bruno & Houard, Xavier & Renner, Ian W., 2020. "Is my sdm good enough? insights from a citizen science dataset in a point process modeling framework," Ecological Modelling, Elsevier, vol. 438(C).
    12. Doko Tchatoka, Firmin & Dufour, Jean-Marie, 2020. "Exogeneity tests, incomplete models, weak identification and non-Gaussian distributions: Invariance and finite-sample distributional theory," Journal of Econometrics, Elsevier, vol. 218(2), pages 390-418.
    13. Jean-Marie Dufour & Joachim Wilde, 2018. "Weak identification in probit models with endogenous covariates," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 611-631, October.
    14. Peter C.B. Phillips, 2001. "Bootstrapping Spurious Regression," Cowles Foundation Discussion Papers 1330, Cowles Foundation for Research in Economics, Yale University.
    15. Chesher, Andrew & Dhaene, Geert & Gouriéroux, Christian & Scaillet, Olivier, 1999. "Bartlett Identities Tests," LIDAM Discussion Papers IRES 1999019, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    16. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2014. "Exact confidence sets and goodness-of-fit methods for stable distributions," Journal of Econometrics, Elsevier, vol. 181(1), pages 3-14.
    17. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, vol. 57(12), pages 2213-2227, December.
    18. Vijay Rajagopal & Gregory Bass & Cameron G Walker & David J Crossman & Amorita Petzer & Anthony Hickey & Ivo Siekmann & Masahiko Hoshijima & Mark H Ellisman & Edmund J Crampin & Christian Soeller, 2015. "Examination of the Effects of Heterogeneous Organization of RyR Clusters, Myofibrils and Mitochondria on Ca2+ Release Patterns in Cardiomyocytes," PLOS Computational Biology, Public Library of Science, vol. 11(9), pages 1-31, September.
    19. Yin, Xiangrong, 2004. "Canonical correlation analysis based on information theory," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 161-176, November.
    20. Jean-Marie Dufour & Lynda Khalaf & Marie-Claude Beaulieu, 2010. "Multivariate residual-based finite-sample tests for serial dependence and ARCH effects with applications to asset pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 263-285.

    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:eee:csdana:v:114:y:2017:i:c:p:75-87. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.