Testing Problems

  • Anirban DasGupta
Part of the Springer Texts in Statistics book series (STS)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Barndorff-Nielsen, O. and Hall, P. (1988). On the level error after Bartlett adjustment of the likelihood ratio statistic, Biometrika, 75, 374–378.zbMATHCrossRefMathSciNetGoogle Scholar
  2. Bartlett, M. (1937). Properties of sufficiency and statistical tests, Proc. R. Soc. London Ser. A, 160, 268–282.Google Scholar
  3. Basu, D. (1955). On statistics independent of a complete sufficient statistic, Sankhya, Ser. A, 15, 377–380.zbMATHGoogle Scholar
  4. Bickel, P.J. and Doksum, K. (2001). Mathematical Statistics: Basic Ideas and Selected Topics, Prentice-Hall, Upper Saddle River, NJ.Google Scholar
  5. Brown, L., Cai, T., and DasGupta, A. (2001). Interval estimation for a binomial proportion, Stat. Sci., 16(2), 101–133.zbMATHMathSciNetGoogle Scholar
  6. Casella, G. and Strawderman, W.E. (1980). Estimating a bounded normal mean, Ann. Stat., 9(4), 870–878.CrossRefMathSciNetGoogle Scholar
  7. Fan, J., Hung, H., and Wong, W. (2000). Geometric understanding of likelihood ratio statistics, J. Am. Stat. Assoc., 95(451), 836–841.zbMATHCrossRefMathSciNetGoogle Scholar
  8. Fan, J. and Zhang, C. (2001). Generalized likelihood ratio statistics and Wilks’ phenomenon, Ann. Stat., 29(1), 153–193.zbMATHCrossRefMathSciNetGoogle Scholar
  9. Ferguson, T.S. (1996). A Course in Large Sample Theory, Chapman and Hall, London.zbMATHGoogle Scholar
  10. Lawley, D.N. (1956). A general method for approximating the distribution of likelihood ratio criteria, Biometrika, 43, 295–303.zbMATHMathSciNetGoogle Scholar
  11. McCullagh, P. and Cox, D. (1986). Invariants and likelihood ratio statistics, Ann. Stat., 14(4), 1419–1430.zbMATHCrossRefMathSciNetGoogle Scholar
  12. Mukerjee, R. and Reid, N. (2001). Comparison of test statistics via expected lengths of associated confidence intervals, J. Stat. Planning Infer., 97(1), 141–151.zbMATHCrossRefMathSciNetGoogle Scholar
  13. Portnoy, S. (1988). Asymptotic behavior of likelihood methods for Exponential families when the number of parameters tends to infinity, Ann. Stat., 16, 356–366.zbMATHCrossRefMathSciNetGoogle Scholar
  14. Rao, C.R. (1948). Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation, Proc. Cambridge Philos. Soc., 44, 50–57.zbMATHMathSciNetCrossRefGoogle Scholar
  15. Robertson, T., Wright, F.T. and Dykstra, R.L. (1988). Order Restricted Statistical Inference, John Wiley, New York.zbMATHGoogle Scholar
  16. Sen, P.K. and Singer, J. (1993). Large Sample Methods in Statistics: An Introduction with Applications, Chapman and Hall, New York.zbMATHGoogle Scholar
  17. Serfling, R. (1980). Approximation Theorems of Mathematical Statistics, Wiley, New York.zbMATHGoogle Scholar
  18. van der Vaart, A. (1998). Asymptotic Statistics, Cambridge University Press, Cambridge.Google Scholar
  19. Wald, A. (1943). Tests of statistical hypotheses concerning several parameters when the number of observations is large, Trans. Am. Math. Soc., 5, 426–482.CrossRefMathSciNetGoogle Scholar
  20. Wilks, S. (1938). The large sample distribution of the likelihood ratio for testing composite hypotheses, Ann. Math. Stat., 9, 60–62.CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Anirban DasGupta
    • 1
  1. 1.Department of StatisticsPurdue UniversityWest Lafayette

Personalised recommendations