Statistical Papers

, Volume 60, Issue 6, pp 2013–2030 | Cite as

Generalized p value for multivariate Gaussian stochastic processes in continuous time

  • Mar FenoyEmail author
  • Pilar Ibarrola
  • Juan B. Seoane-Sepúlveda
Regular Article


We construct a Generalized p value for testing statistical hypotheses on the comparison of mean vectors in the sequential observation of two continuous time multidimensional Gaussian processes. The mean vectors depend linearly on two multidimensional parameters and with different conditions about their covariance structures. The invariance of the generalized p value considered is proved under certain linear transformations. We report results of a simulation study showing power and errors probabilities for them. Finally, we apply our results to a real data set.


Generalized p value Hypothesis testing Continuous time Multivariate Behrens–Fisher problem 

Mathematics Subject Classification

Primary: 62M09 Secondary: 62H12 



The authors thank the anonymous referees for their helpful comments and suggestions. The first and third authors were supported by MTM2015-65825-P


  1. Akahira M (2002) Confidence intervals for the difference of means: application to the Behrens–Fisher type problem. Stat Pap 43(2):273–284MathSciNetCrossRefGoogle Scholar
  2. Bacanli S, Demirhan YP (2008) A group sequential test for the inverse Gaussian mean. Stat Pap 49(2):377–386MathSciNetCrossRefGoogle Scholar
  3. Gamage JK (1997) Generalized \(p\) values and the multivariate Behrens–Fisher problem. Linear Algebra Appl 253:369–377MathSciNetCrossRefGoogle Scholar
  4. Gamage JK, Mathew T, Weerahandi S (2004) Generalized \(p\) values and generalized confidence regions for the multivariate Behrens–Fisher problem and MANOVA. J Multivar Anal 88(1):177–189MathSciNetCrossRefGoogle Scholar
  5. Ibarrola P, Vélez R (2002) Testing and confidence estimation of the mean of a multidimensional Gaussian process. Statistics 36(4):317–327MathSciNetCrossRefGoogle Scholar
  6. Ibarrola P, Vélez R (2004) On Behrens–Fisher problem for continuous time Gaussian processes. Linear Algebra Appl 389:63–76MathSciNetCrossRefGoogle Scholar
  7. Johnson NL, Kotz S, Balakrishnan N (1994) Continuous univariate distributions, vol. 1, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. John Wiley & Sons, Inc., New YorkGoogle Scholar
  8. Lin SH, Lee JC, Wang RS (2007) Generalized inferences on the common mean vector of several multivariate normal populations. J Stat Plan Inference 137(7):2240–2249MathSciNetCrossRefGoogle Scholar
  9. Park Junyong (2010) The generalized \(p\) value in one-sided testing in two sample multivariate normal populations. J Stat Plan Inference 140(4):1044–1055MathSciNetCrossRefGoogle Scholar
  10. Park J, Sinha B (2009) Some aspects of multivariate Behrens–Fisher problem. Calcutta Stat Assoc Bull 61(241–244):125–141MathSciNetCrossRefGoogle Scholar
  11. Salau MO (2003) The effects of different choices of order for autoregressive approximation on the Gaussian likelihood estimates for ARMA models. Stat Pap 44(1):89–105MathSciNetCrossRefGoogle Scholar
  12. Tsui KW, Weerahandi S (1989) Generalized \(p\) values in significance testing of hypotheses in the presence of nuisance parameters. J Am Stat Assoc 84(406):602–607MathSciNetGoogle Scholar
  13. Weerahandi S (1993) Generalized confidence intervals. J Am Stat Assoc 88(423):899–905MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Mar Fenoy
    • 1
    Email author
  • Pilar Ibarrola
    • 1
  • Juan B. Seoane-Sepúlveda
    • 2
  1. 1.Departamento de Estadística e Investigación Operativa, Facultad de Ciencias MatemáticasUniversidad Complutense de MadridMadridSpain
  2. 2.Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI)Universidad Complutense de MadridMadridSpain

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