Zastosowanie algorytmu EM do estymacji parametrów rozkładu na podstawie danych pogrupowanych

• Autorzy: Roman Huptas

Warianty tytułu

The Application of the EM Algorithm to Estimation of Parameters of Distribution in Case Data are Grouped

• Języki publikacji: PL

Abstrakty

Podjęto problem maksymalizacji wiarygodnościowej funkcji oceny, kiedy w zbiorze danych występują zmienne, a ich wartości z jakichś powodów nie zostały zaobserwowane. Opisano algorytm EM oraz przykład jego zastosowania.

EN

In this article, the Expectation-Maximization (EM) algorithm and its application are presented. The EM algorithm is a powerful iterative technique for finding maximum likelihood estimates, which is useful in a wide variety of situations best described as "incomplete data problems", where algorithms such as the Newton-Raphson method may turn out to be more complicated. The popularity of the EM algorithm arises from its simplicity in implementation, stability in convergence, and applicability in practice. In the article, the E-step and M-step of the EM algorithm are illustrated with an application. The application is related to estimating parameters of distribution in case data are grouped and possibly truncated. The author presents the results of a simulation experiment in which the sizes of the Pearson chi-square goodness of fit test are obtained in two cases: when the unknown parameters are estimated from grouped data by means of the EM algorithm (correct procedure) and when original, ungrouped data are used (a wrong but frequently used procedure). (original abstract)

Słowa kluczowe

PL

Statystyka matematyczna; Estymacja; Algorytmy

EN

Mathematical statistics; Estimation; Algorithms

• Czasopismo: Zeszyty Naukowe / Akademia Ekonomiczna w Krakowie
• Rocznik: 2007
• Numer: nr 740
• Strony: 131--145

Twórcy

autor

Roman Huptas

Bibliografia

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• Magiera R. [200], Modele i metody statystyki matematycznej, wyd. l, GiS, Wrocław.
• McLachlan G. J., Krishnan T. [1997], The EM Algorithm and Extensions, John Wiley and Sons, New York.
• Press W.H., Teukolsky S.A., Vetterling W.T., FJannery B.R [1995], Numerical Recipes in C. The Art of Scientific Computing, Cambridge University Press, New York.
• Wu C.F.J. [I983] On the Convergence Properties of the EM Algorithm, „Annals of Statistics", vol. 11.