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Huptas Roman (Kolegium Ekonomii, Finansów i Prawa)
Zastosowanie algorytmu EM do estymacji parametrów rozkładu na podstawie danych pogrupowanych
The Application of the EM Algorithm to Estimation of Parameters of Distribution in Case Data are Grouped
Zeszyty Naukowe / Akademia Ekonomiczna w Krakowie, 2007, nr 740, s. 131-145, bibliogr. 6 poz.
Statystyka matematyczna, Estymacja, Algorytmy
Mathematical statistics, Estimation, Algorithms
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.

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)
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  2. Dempster A.P., Laird N.M, Rubin D.B. [1977], Maximum Likelihood from Incomplete Data via the EM Algorithm (with Discussion), „Journal of the Royal Statistical Society B" vol. 39.
  3. Magiera R. [200], Modele i metody statystyki matematycznej, wyd. l, GiS, Wrocław.
  4. McLachlan G. J., Krishnan T. [1997], The EM Algorithm and Extensions, John Wiley and Sons, New York.
  5. 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.
  6. Wu C.F.J. [I983] On the Convergence Properties of the EM Algorithm, „Annals of Statistics", vol. 11.
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