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Journal of Statistical Theory and Practice

, Volume 2, Issue 3, pp 385–406 | Cite as

On the Efficiency of a Semiparametric Approach to the One-Way Layout

  • Richard Gagnon
  • Benjamin Kedem
  • Ying Qi
Article

Abstract

A semiparametric approach to the one-way layout is described, and its efficiency in the two-sample case relative to the common t-test is studied. The power efficiency computed for several special cases points to an intriguing behavior where one test can be more efficient than the other over a certain parameter range and less efficient over some other range. Given m random samples from m distributions, the method holds one distribution as “reference” and treats the other distributions as “distortions” of the reference. The combined sample is used in the semiparametric estimation of the reference distribution and its distortions, and in testing the hypothesis of distribution equality. An application to microarray data illustrates the main ideas, and also motivates the question of power efficiency.

AMS Subject Classification

Primary 62F05 Secondary 62F10 92B05 

Keywords

Profile likelihood hypothesis test exponential distortion Pitman efficiency gene expression cDNA 

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References

  1. Alizadeh, A.A., Eisen, M.B., Davis, R.E., Ma, C., Lossos, I.S., Rosenwald, A., Boldrick, J.C., Sabet, H., Tran, T., Yu, X., Powell, J.I., Yang, L., Marti, G.E., Moore, T., Hudson, J. Jr, Lu, L., Lewis, D.B., Tibshirani, R., Sherlock, G., Chan, W.C., Greiner, T.C., Weisenburger, D.D., Armitage, J.O., Warnke, R., Levy, R., Wilson, W., Grever, M.R., Byrd, J.C., Botstein, D., Brown, P.O., Staudt, L.M., 2000. Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling. Nature, 403, 503–511.CrossRefGoogle Scholar
  2. Beibarth, T., Fellenberg, K., Brors, B., Arribas-Prat, R., Boer, J. M., Hauser, N. C., Scheideler, M., Hoheisel, J. D., Schütz, G., Poustka, A., Vingron, M., 2000. Processing and quality control of DNA array hybridization data. Bioinformatics, 16, 1014–1022.CrossRefGoogle Scholar
  3. Bickel, P.J., Doksum, K.A., 1977. Mathematical Statistics. Holden Day, San Francisco.zbMATHGoogle Scholar
  4. Casella, G., Berger, R., 1990. Statistical Inference. Duxbury Press, Belmont.zbMATHGoogle Scholar
  5. Fokianos, K., 2004. Merging information for semiparametric density estimation. Journal of the Royal Statistical Society B, 66, 941–958.MathSciNetCrossRefGoogle Scholar
  6. Fokianos, K., Kedem, B., Qin, J., Short, D.A., 2001. A semiparametric approach to the one-way layout. Technometrics, 43, 56–65.MathSciNetCrossRefGoogle Scholar
  7. Gagnon, R., 2005. Computational Aspects of Power Efficiency and State Space Models. PhD Dissertation, University of Maryland, College Park.Google Scholar
  8. Gilbert, P.B., Lele, S.R., Vardi, Y., 1999. Maximum likelihood estimation in semiparametric selection bias models with application to AIDS vaccine trials. Biometrika, 86, 27–43.MathSciNetCrossRefGoogle Scholar
  9. Gilbert, P.B., 2000. Large sample theory of maximum likelihood estimates in semiparametric biased sampling models. Annals of Statistics, 28, 151–194.MathSciNetCrossRefGoogle Scholar
  10. Kedem, B., Wen, S., 2007. Semi-parametric cluster detection. Journal of Statistical Theory and Practice, 1 (1), 49–72.MathSciNetCrossRefGoogle Scholar
  11. Lockhart, D.J., Winzeler, E.A., 2000. Genomics, gene expression and DNA arrays. Nature, 405, 827–836.CrossRefGoogle Scholar
  12. Patil, G.P., Rao, C.R., 1977. The weighted distributions: A survey of their applications. Applications of Statistics, Ed. P.R. Krishnaiah, 383–405. Amsterdam: North-Holland.Google Scholar
  13. Qi, Y., 2002. Classification of Microarray Data. MA Thesis, University of Maryland, College Park.Google Scholar
  14. Qin, J., 1998. Inferences for case-control and semiparametric two-sample density ratio models. Biometrika, 85, 619–630.MathSciNetCrossRefGoogle Scholar
  15. Qin, J., Zhang, B., 1997. A goodness of fit test for logistic regression models based on case-control data. Biometrika, 84, 609–618.MathSciNetCrossRefGoogle Scholar
  16. van der Vaart, A.W., 1998. Asymptotic Statistics. Cambridge University Press, Cambridge.CrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Core Genotyping FacilitySAIC-Frederick, Inc.GaithersburgUSA

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