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Computing Critical Values of Exact Tests by Incorporating Monte Carlo Simulations Combined with Statistical Tables

Author

Listed:
  • Albert Vexler
  • Young Min Kim
  • Jihnhee Yu
  • Nicole A. Lazar
  • Alan D. Hutson

Abstract

type="main" xml:id="sjos12079-abs-0001"> Various exact tests for statistical inference are available for powerful and accurate decision rules provided that corresponding critical values are tabulated or evaluated via Monte Carlo methods. This article introduces a novel hybrid method for computing p-values of exact tests by combining Monte Carlo simulations and statistical tables generated a priori. To use the data from Monte Carlo generations and tabulated critical values jointly, we employ kernel density estimation within Bayesian-type procedures. The p-values are linked to the posterior means of quantiles. In this framework, we present relevant information from the Monte Carlo experiments via likelihood-type functions, whereas tabulated critical values are used to reflect prior distributions. The local maximum likelihood technique is employed to compute functional forms of prior distributions from statistical tables. Empirical likelihood functions are proposed to replace parametric likelihood functions within the structure of the posterior mean calculations to provide a Bayesian-type procedure with a distribution-free set of assumptions. We derive the asymptotic properties of the proposed nonparametric posterior means of quantiles process. Using the theoretical propositions, we calculate the minimum number of needed Monte Carlo resamples for desired level of accuracy on the basis of distances between actual data characteristics (e.g. sample sizes) and characteristics of data used to present corresponding critical values in a table. The proposed approach makes practical applications of exact tests simple and rapid. Implementations of the proposed technique are easily carried out via the recently developed STATA and R statistical packages.

Suggested Citation

  • Albert Vexler & Young Min Kim & Jihnhee Yu & Nicole A. Lazar & Alan D. Hutson, 2014. "Computing Critical Values of Exact Tests by Incorporating Monte Carlo Simulations Combined with Statistical Tables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1013-1030, December.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:4:p:1013-1030
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    File URL: http://hdl.handle.net/10.1111/sjos.12079
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    References listed on IDEAS

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    1. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
    2. Vexler, Albert & Gurevich, Gregory, 2010. "Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 531-545, February.
    3. Wang Zhou & Bing-Yi Jing, 2003. "Adjusted empirical likelihood method for quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 689-703, December.
    4. Paul R. Rosenbaum, 2005. "An exact distribution‐free test comparing two multivariate distributions based on adjacency," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 515-530, September.
    5. Jihnhee Yu & Albert Vexler & Lili Tian, 2010. "Analyzing Incomplete Data Subject to a Threshold using Empirical Likelihood Methods: An Application to a Pneumonia Risk Study in an ICU Setting," Biometrics, The International Biometric Society, vol. 66(1), pages 123-130, March.
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    1. Hadi Alizadeh Noughabi & Albert Vexler, 2016. "An efficient correction to the density-based empirical likelihood ratio goodness-of-fit test for the inverse Gaussian distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(16), pages 2988-3003, December.
    2. Hadi Alizadeh Noughabi, 2015. "Empirical likelihood ratio-based goodness-of-fit test for the logistic distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 1973-1983, September.

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