Asymptotic properties of the ANOVA test under general loss functions

• Autorzy: Adamczyk Katarzyna

Identyfikatory

DOI

10.14708/ma.v22i36.1818

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

quadratic function; variance; covariance

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Matematyka Stosowana : matematyka dla społeczeństwa
• Rocznik: 1993
• Tom: Nr 36
• Strony: 75--97
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Adamczyk Katarzyna

Bibliografia

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• [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).