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Introduction to Non-parametric Theories

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Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 202)

Abstract

In the previous chapters we have frequently made use of the assumption that the set Γ of parameters is a (open or closed) subset of R n, n⩽1. In addition, in connection with essential results, we have imposed continuity and differentiability requirements on the likelihood function. For some time, so-called non-parametric methods have received considerable attention. Their beginnings, however, lie far in the past. Recent progress is due to Anglo-american, Dutch and Soviet statisticians. The term “non-parametric” is rather unfortunately chosen and it is not easy to give a satisfactory definition of this notion. Roughly speaking, one can call a test or method of estimation nonparametric when no assumptions such as those above are made o n Γ 2 .

Keywords

Null Hypothesis Probability Measure Order Statistic Stochastic Approximation Empirical Distribution Function 
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Copyright information

© Springer-Verlag Berlin · Heidelberg 1974

Authors and Affiliations

  1. 1.University of ViennaAustria

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