Národní úložiště šedé literatury Nalezeno 73 záznamů.  1 - 10dalšíkonec  přejít na záznam: Hledání trvalo 0.01 vteřin. 
Introduction to statistical inference based on scalar-valued scores
Fabián, Zdeněk
In the report we maintain consistently the following point of view: Given a continuous model, there are not the observed values, which are to be used in probabilistic and statistical considerations, but their ”treated forms”,the values of the scalar-valued score function corresponding to the model. Based on this modified concept of the score function, we develop theory of score random variables, study their geometry and define their new characteristics, finite even in cases of heavy-tailed models. A generalization for parametric families provides a new approach to parametric point estimation.
A New Look to Information and Uncertainty of Continuous Distributions
Fabián, Zdeněk
We define information and uncertainty function of a family of continuous distributions. Their values are relative information and uncertainty of an observation from the given parametric family, their mean values are the generalized Fisher information and a new measure of variability, the score variance. In a series of examples we show why to use new concepts instead of the differential entropy.
Score correlation for skewed distributions
Fabián, Zdeněk
Based on the new concept of the scalar-valued score function of continuous distributions we introduce the score correlation coefficient ”tai-lored” to the assumed probabilistic model and study its properties by means of simulation experiments. It appeared that the new correlation method is useful for enormously skewed distributions.
Scalar-Valued Score Functions and their use in Parametric Estimation
Fabián, Zdeněk
In the paper we describe and explain a new direction in probabilistic and statistical reasoning, the approach based on scalar-valued score functions of continuous random variables. We show basic properties of score functions of standard distributions, generalize the approach for parametric families and show how to use them for solutions of problems of parametric statistics.
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A Measure of Variability WIthin Parametric Families of Continuous Distributions
Fabián, Zdeněk
A continuous probability measure on an open interval of the real line induces in it a unique geometry, "center of gravity" of which is the typical value of the distribution. In the paper is identified a score variance as a finite measure of variability of distributions with respect to the typical value and discussed its properties and methods of estimation. Itroducing a generalized Rao distance in the sample space one can appraise the precision of the estimate of the typical value.
The scalar-valued score functions of continuous probability distribution
Fabián, Zdeněk
In this report we give theoretical basis of probability theory of continuous random variables based on scalar valued score functions. We maintain consistently the following point of view: It is not the observed value, which is to be used in probabilistic and statistical considerations, but its 'treated form', the value of the scalar-valued score function of distribution of the assumed model. Actually, the opinion that an observed value of random variable should be 'treated' with respect to underlying model is one of main ideas of the inference based on likelihood in classical statistics. However, a vector nature of Fisher score functions of classical statistics does not enable a consistent use of this point of view. Instead, various inference functions are suggested and used in solutions of various statistical problems. Inference function of this report is the scalar-valued score function of distribution.

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