A note on the maximum likelihood estimator in the gamma regression model

• Autorzy: Rydlewski J. P.
• Języki publikacji: EN

Abstrakty

EN

This paper considers a nonlinear regression model, in which the dependent variable has the gamma distribution. A model is considered in which the shape parameter of the random variable is the sum of continuous and algebraically independent functions. The paper proves that there is exactly one maximum likelihood estimator for the gamma regression model.

Słowa kluczowe

EN

gamma regression; nonlinear regression; maximum likelihood estimator; shape parameter

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2009
• Tom: Vol. 29, no. 3
• Strony: 305--312
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Rydlewski J. P.

• AGH University of Science and Technology Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Krakow, Poland Jagiellonian University Department of Mathematics ul. Łojasiewicza 6, 30-348 Krakow, Poland,

Bibliografia

• [1] K.O. Bowman, L.R. Shenton, Properties of Estimators for the Gamma Distribution, Marcel Dekker, New York, 1988.
• [2] F. Cribari–Neto, K.L.P. Vasconcellos, Nearly unbiased maximum likelihood estimation for the beta distribution, J. Stat. Comput. Simul. 72 (2002), 107–118.
• [3] J.P. Rydlewski, Beta–regression model for periodic data with a trend, Univ. Iage. Acta. Math. XLV (2007), 211–222.
• [4] G.A.F. Seber, C.J. Wild, Nonlinear Regression, Wiley, New York, 2003.
• [5] R.W.M. Wedderburn, On the existence and uniqueness of the maximum likelihood estimates for certain generalized linear models, Biometrika 63 (1976), 27–32.
• [6] B.C. Wei, Exponential Family Nonlinear Models, Springer, Singapore, 1998.