The scalar-valued score functions of continuous probability distribution

0503653 - ÚI 2020 CZ eng V - Výzkumná zpráva
Fabián, Zdeněk
The scalar-valued score functions of continuous probability distribution.
Prague: ICS CAS, 2019. 71 s. Technical Report, V-1264.
Institucionální podpora: RVO:67985807
Klíčová slova: Shortcomings of probability theory * Scalar-valued score functions * Characteristics of continous random variables * Parametric estimation * Transformed distributions * Skew-symmetric distributions

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.
Trvalý link: http://hdl.handle.net/11104/0295464