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Statistical Decision Rules and Optimal Inference by Nikolai Nikolaevich Cencov

24 February 2017 adminProbability Statistics

By Nikolai Nikolaevich Cencov

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16. , Sidak, Z. and Sen, P. K. (1999). Theory of Rank Tests, 2nd Ed. Academic Press, London. 17. Hodges, J. L. and Lehmann, E. L. (1963). Estimates of location based on rank tests. Ann. Math. Statist. 34, 598–611. 18. Hoeffding, W. (1948). A class of statistics with asmptotically normal distribution. Ann. Math. Statist. 19, 293–325. 19. Huber, P. J. (1964). Robust estimation of a location parameter. Ann. Math. Statist. 35, 73–101. 20. Huber, P. J. and Ronchetti, E. M. (2009). Robust Statistics, 2nd Ed.

In Statist. 3, 37–98. 27. Mosteller, F. (1948). A k-sample slippage test for an extreme population. Ann. Math. Statist. 19, 58–65. 28. Murphy, S. A. and Sen, P. K. (1991). Cox regression model with timedependent covariates. Stochastic Process. Appl. 39, 153–180. 29. Nadaraya, E. A. (1964). On estimating regression. Theor. Probab. Applicat. 9, 141–142. 30. Pitman, E. J. G. (1948). Lecture Notes, Columbia Univ. 31. Puri, M. L. and Sen, P. K. (1971). Nonparametric Methods in Multivariate Analysis.

1. Introduction Prior to 1960s, nonparametrics, usually referred to as distribution-free or rank based methods, were mostly confined to specific simple models where suitable hypotheses of invariance led to statistical inference (mostly, testing) procedures without explicitly assuming the form of underlying distributions (as is customarily the case in parametric statistical inference).

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