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The author studies the classical analysis of variance problem under nonnormal distributions involving a location parameter (so that these distributions really do not involve an unknown variance). The quadratic function in the analysis of variance decomposition is replaced by a convex even function w, and the asymptotic distribution of the corresponding test statistic under the null hypothesis is found to be a chi-squared distribution. Several specific choices of w are considered in detail.
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Tom
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75--97
Opis fizyczny
Bibliogr. 10 poz.
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autor
Bibliografia
- [1] Z. D. Bai, C. R. Rao and Y. Q. Yin, Y.Q. (1990). Least absolute deviations analysis of variance, Sankhya 52, A, (1990), 166-177.
- [2] P. Milasevic and G. R. Ducharme, Uniqueness of the spatial median, Ann. Statist. 15, (1987), 1332-1333.
- [3] R. Koenker, Asymptotic testing methods for L1-regression, in Statistical Data Analysis Based on L1-norm, Y. Dodge (ed.), North Holland, (1987).
- [4] J. W. McKean and R. M. Schrader, Least Absolute Errors Analysis of Variance, W Statistical Data Analysis Based on L1-norm, Y. Dodge (ed.), North Holland.
- [5] W. Niemiro, Asymptotics for M-estimators defined by convex minimization, Ann. Statist. (1992a) (to appear).
- [6] W. Niemiro, Least empirical risk procedures in statistical inference, Statistical Data Analysis Based on L1-norm, Y. Dodge (ed.) (1992b) (to appear).
- [7] D. Pollard, Convergence of Stochastic Processes, Springer, (1984).
- [8] C. R. Rao, Methodology based on the L1-norm in statistical inference, Sankhya, 50, A, (1988) 289-313.
- [9] S. D. Silvey, Statistical Inference, (1970).
- [10] R. J. Serfling, Approximation Theorems of Mathematical Statistics, Wiley, (1980).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-706ce682-82d4-4511-b3fe-471ba48cabb3