This paper is concerned with the study of some properties of the distance between statistical individuals based on representations on the dual tangent space of a parametric manifold representation of a statistical model. Explicit expressions for distances are obtained for well-known families of distributions. We have also considered applications of the distance to parameter estimation, testing statistical hypotheses and discriminant analysis.
In this paper we review different meanings of the word intrinsic in statistical estimation, focusing our attention on the use of this word in the analysis of the properties of an estimator. We review the intrinsic versions of the bias and the mean square error and results analogous to the Cramér-Rao inequality and Rao-Blackwell theorem. Different results related to the Bernoulli and normal distributions are also considered.
En este trabajo se describe una metodología que nos permite representar simultáneamente poblaciones estadísticas y variables aleatorias, así como transformaciones admisibles de las mismas. Para ello se representan las variables aleatorias, o sus transformadas, en el espacio tangente a la variedad de las poblaciones estadísticas, a continuación se proyectan en dicha variedad y, finalmente, se aplica un análisis canónico de poblaciones para su representación en un espacio de dimensión reducida. Los...
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