Substantiation of the Maximum Likelihood Method as a Theoretic Statistical Tool for Economic Data Assessment

This study describes two extreme cases of the assessment of data that can have economic value. The data are assessed using a formal application of the maximum likelihood method, which is used extensively in theoretical and applied statistics. Aim. The study aims to describe two assessment cases-discrete and continuous-that are presented in the form of procedures used to determine the parameter that is used to assess the amount of data obtained from an arbitrarily set statistical sample recorded through observations of a mass phenomenon or process. Tasks. The study provides an interpretation of this research using modern mathematics and a set of mathematical and instrumental economic procedures that allow a modern theoretical economist to become oriented in the methodological constructions providing an understanding of the subject and methods of modern economic research applied to the complex processes of data assessment. Methods. Methodologically, the differences in the study of the maximum likelihood method for discrete and continuous processes are thoroughly analyzed. It is shown that in extreme cases of transition, discrete and continuous are a certain unity of the mathematical continuum, which is recorded in the study. Results. The author concludes that the maximum likelihood method suggests that the minimum value θ , which provides a positive probability density of the examined sample values, should be selected as the likelihood function argument. The resulting assessment of the specified parameter makes it possible to extract the required amount of data from the sample. Conclusions. The limiting law for a normal p -vector sample space H n is the p -dimensional normal law determined by a special covariance matrix J . Since the sample components in applied economic problems have embodied or material meaning, the obtained data eventually make it possible to control set economic systems in certain conditions, even under uncertainty.

statistical sample, distribution function, discrete and continuous distribution, likelihood function, amount of data, economic interpretation of data, статистическая выборка, функция распределения, дискретные и непрерывные распределения, функция правдоподобия, количество информации, экономическая интерпретация информации

1. Levy P. Theorie de l’Addition des Variables Aleatoires. 2nd ed. Paris: Gauthier-Villars, 1954. 334 p.

2. Blanc-Lapierre A., Fortet R. Theorie des Fonctions Aleatoires. Paris: Masson et Cie., 1953. 694 p.

3. Frechet M. Generalites sur les probabilites. Elements aleatoires. 2nd ed. Paris: Gauthier-Villars, 1950. 355 p.

4. Borel E. et autres. Traite du Calcul des Probabilites et de ses application. 4 volumes. Paris: Gauthier-Villars, 1952.