Abstract
Huber and Strassen have shown in [2] that a composite testing problem can be replaced by an equivalent single one (in terms of least favourable pairs of distributions), when both hypotheses are given by 2-alternating capacities. In this paper a rather general technique is presented in order to construct the least favourable distribution, if one of the hypotheses is a simple one. The mentioned technique applies not only to the total-variation and the ε-contamination model but also to Prochorov-neighbourhoods of distributions on the real line.
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References
Huber, P.J.: A robust version of the probability ratio test, Ann. Math. Stat. 35 (1965), 73–101.
Huber, P.J. and V. Strassen: Minimax tests and Neyman-Pearson lemma for capacities, Ann. Stat. 1 (1973), 251–263 and Ann. Stat. 2 (1974), 223–224.
Rieder, H.: Zur finiten und asymptotischen Theorie robuster Tests, Dissertation, Albert-Ludwigs-Universität Freiburg i. Br. (1976).
Ă–sterreicher, F.: On the construction of least favourable pairs of distributions, submitted to Z. f. Wahrscheinlichkeitstheorie verw. Geb. (1976).
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© 1978 Springer-Verlag
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Österreicher, F. (1978). On the construction of least favourable distributions. In: Kallianpur, G., Kölzow, D. (eds) Measure Theory Applications to Stochastic Analysis. Lecture Notes in Mathematics, vol 695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062672
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DOI: https://doi.org/10.1007/BFb0062672
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