Abstract
For n = 1, 2, … let (X n1, A n1), …, (X nn , A nn ) be arbitrary measurable spaces. Let P ni and Q ni be probability measures defined on (X ni , A ni ), i = 1, …, n; n = 1, 2, …, and let \(P_n^{\left( n \right)} = \prod\limits_{i = 1}^n {{P_{ni}}}\) and \(Q_n^{\left( n \right)} = \prod\limits_{i = 1}^n {{Q_{ni}}}\) denote the product probability measures. For each i and n let X ni be the identity map from X ni onto X ni . Then P ni and Q ni represent the two possible distributions of the random element X ni as well as the probability measures of the underlying probability space. Obviously X n1, …, X nn are independent under both \(P_n^{\left( n \right)}\) and \(Q_n^{\left( n \right)}\) (n = 1, 2, …).
Report SW 36/75 Mathematisch Centrum, Amsterdam
AMS (MOS) subject classification scheme (1970): 62E20
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HAJEK, J.- SmAK, Z. (1967). "Theory of rank tests". Academic Press, New York.
LE CAM, L. (1960). Locally asymptotically normal families of distributions. Univ. California Pub/. Statist., 3, 37-98, University of California Press.
LE CAM, L. (1966). Likelihood functions for large numbers of independent observations. Research papers in statistics (Festschrift for J. Neyman), 167-187, F. N. David (ed.), Wiley, New York.
LE CAM, L. (1969). Theorie asymptotique de la decision statistique. Les Presses de l'Universite de Montreal.
LOEVE, M. (1963). "Probability theory (3rd ed.)". Van Nostrand, New York.
RoussAS, G. G. (1972). Contiguity of probability measures: some applications in statistics, Cambridge University Press.
WITTING, H.- NoLLE G. (1970). "Angewandte mathematische Statistik". Teubner, Stuttgart.
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Oosterhoff, J., van Zwet, W.R. (2012). A Note on Contiguity and Hellinger Distance. In: van de Geer, S., Wegkamp, M. (eds) Selected Works of Willem van Zwet. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1314-1_6
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