Generalised score and Wald tests. (English) Zbl 1189.62029
Summary: The generalised score and Wald tests are described and related to their non-generalised versions. Two interesting applications are discussed. In the first, a new test for the Behrens-Fisher problem is derived. The second is testing homogeneity of variances from multiple univariate normal populations.
MSC:
| 62F03 | Parametric hypothesis testing |
References:
| [1] | J. C. W. Rayner, “The asymptotically optimal tests,” Journal of the Royal Statistical Society Series D, vol. 46, no. 3, pp. 337-346, 1997. · doi:10.1111/1467-9884.00087 |
| [2] | J. C. W. Rayner, O. Thas, and D. J. Best, Smooth Tests of Goodness of Fit: Using R, John Wiley & Sons, Singapore, 2nd edition, 2009. · Zbl 1171.62015 |
| [3] | A. W. van der Vaart, Asymptotic Statistics, vol. 3 of Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge, UK, 1998. · Zbl 0910.62001 |
| [4] | J. T. Kent, “Robust properties of likelihood ratio tests,” Biometrika, vol. 69, no. 1, pp. 19-27, 1982. · Zbl 0485.62031 |
| [5] | D. Boos, “On generalised score tests,” The American Statistician, vol. 47, pp. 327-333, 1992. |
| [6] | H. White, “Maximum likelihood estimation of misspecified models,” Econometrica, vol. 50, no. 1, pp. 1-25, 1982. · Zbl 0478.62088 · doi:10.2307/1912526 |
| [7] | B. L. Welch, “The significance of the difference between two means when the population variances are unequal,” Biometrika, vol. 29, pp. 350-362, 1937. · Zbl 0018.22602 · doi:10.1093/biomet/29.3-4.350 |
| [8] | P. Rippon, J. Rayner, and O. Thas, “A competitor for the test Welch test in the Behrens-Fisher problem,” Unpublished Report, 2008. |
| [9] | J. L. Goldberg, Matrix Theory with Applications, McGraw-Hill, New York, NY, USA, 1991. · Zbl 0746.90055 |
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