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Testing Problems

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References

  • Barndorff-Nielsen, O. and Hall, P. (1988). On the level error after Bartlett adjustment of the likelihood ratio statistic, Biometrika, 75, 374–378.

    Article  MATH  MathSciNet  Google Scholar 

  • Bartlett, M. (1937). Properties of sufficiency and statistical tests, Proc. R. Soc. London Ser. A, 160, 268–282.

    Google Scholar 

  • Basu, D. (1955). On statistics independent of a complete sufficient statistic, Sankhya, Ser. A, 15, 377–380.

    MATH  Google Scholar 

  • Bickel, P.J. and Doksum, K. (2001). Mathematical Statistics: Basic Ideas and Selected Topics, Prentice-Hall, Upper Saddle River, NJ.

    Google Scholar 

  • Brown, L., Cai, T., and DasGupta, A. (2001). Interval estimation for a binomial proportion, Stat. Sci., 16(2), 101–133.

    MATH  MathSciNet  Google Scholar 

  • Casella, G. and Strawderman, W.E. (1980). Estimating a bounded normal mean, Ann. Stat., 9(4), 870–878.

    Article  MathSciNet  Google Scholar 

  • Fan, J., Hung, H., and Wong, W. (2000). Geometric understanding of likelihood ratio statistics, J. Am. Stat. Assoc., 95(451), 836–841.

    Article  MATH  MathSciNet  Google Scholar 

  • Fan, J. and Zhang, C. (2001). Generalized likelihood ratio statistics and Wilks’ phenomenon, Ann. Stat., 29(1), 153–193.

    Article  MATH  MathSciNet  Google Scholar 

  • Ferguson, T.S. (1996). A Course in Large Sample Theory, Chapman and Hall, London.

    MATH  Google Scholar 

  • Lawley, D.N. (1956). A general method for approximating the distribution of likelihood ratio criteria, Biometrika, 43, 295–303.

    MATH  MathSciNet  Google Scholar 

  • McCullagh, P. and Cox, D. (1986). Invariants and likelihood ratio statistics, Ann. Stat., 14(4), 1419–1430.

    Article  MATH  MathSciNet  Google Scholar 

  • 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.

    Article  MATH  MathSciNet  Google Scholar 

  • Portnoy, S. (1988). Asymptotic behavior of likelihood methods for Exponential families when the number of parameters tends to infinity, Ann. Stat., 16, 356–366.

    Article  MATH  MathSciNet  Google Scholar 

  • 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.

    Article  MATH  MathSciNet  Google Scholar 

  • Robertson, T., Wright, F.T. and Dykstra, R.L. (1988). Order Restricted Statistical Inference, John Wiley, New York.

    MATH  Google Scholar 

  • Sen, P.K. and Singer, J. (1993). Large Sample Methods in Statistics: An Introduction with Applications, Chapman and Hall, New York.

    MATH  Google Scholar 

  • Serfling, R. (1980). Approximation Theorems of Mathematical Statistics, Wiley, New York.

    MATH  Google Scholar 

  • van der Vaart, A. (1998). Asymptotic Statistics, Cambridge University Press, Cambridge.

    Google Scholar 

  • Wald, A. (1943). Tests of statistical hypotheses concerning several parameters when the number of observations is large, Trans. Am. Math. Soc., 5, 426–482.

    Article  MathSciNet  Google Scholar 

  • Wilks, S. (1938). The large sample distribution of the likelihood ratio for testing composite hypotheses, Ann. Math. Stat., 9, 60–62.

    Article  MATH  Google Scholar 

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DasGupta, A. (2008). Testing Problems. In: Asymptotic Theory of Statistics and Probability. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-75971-5_21

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