Nonparametric Statistical Data Science: A Unified Approach Based on Density Estimation and Testing for 'White Noise'.
STATE UNIV OF NEW YORK AT BUFFALO AMHERST STATISTICAL SCIENCE DIV
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This paper proposes an approach to non-parametric statistical continuous data science which seems to be consistent with the conventional theories and methods of non-parametric inference but seems to point the way to universally applicable procedures for continuous data which are asymptotically as efficient as the best conventional goodness of fit and parameter estimation procedures available for each particular problem. The methods described are programmed and found successful in test cases. However, in the space available here only Chapter 1 of this work can be discussed. It outline the ideas how the basic general applied problems of statistical inference can be formulated as problems of estimation of distribution functions on the unit interval or the unit hyper-cube, how such problems are more fruitfully treated as density estimation problems, and how to solve density estimation problems one can use the method which is the essence of the highly successful maximum likelihood method of parameter estimation using a suitable information-theoretic divergence distance between densities, find the smooth density which is closest to a raw estimator of the density.
- Statistics and Probability