Summary
The multiparameter exponential families of probability density functions include many commonly used densities such as the normal, gamma, and beta, and many others besides. We consider the general parameter estimation problem for these families, given observations that are restricted (i.e. truncated) to the closed interval [a,b]. We show how to find maximum likelihood estimators using Newton-Raphson iteration, but observe that in general this technique requires numerical integration within each iteration. Then we give a new non-iterative method for obtaining the desired estimators for the parameter vector. An example using the generalized Inverse Gaussian is given.
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References
Barndorff-Nielsen, O. (1978). Information and Exponential Families in Statistical Theory. Wiley, New York.
Crain, B.R. (1976). Exponential models, maximum likelihood estimation, and the Haar condition. Journal of the American Statistical Association, 71, 737–740.
Lehman, E.L. (1959). Testing Statistical Hypotheses. Wiley, New York.
Wilks, S.S. (1962). Mathematical Statistics. Wiley, New York.
Yang, G.L., Chen, T.C. (1978). On statistical methods of neuronal spike-train analysis. Mathematical Biosciences, 38, 1–34.
Zangwill, W.I. (1969). Nonlinear Programming: A Unified Approach. Prentice-Hall, Englewood Cliffs, New Jersey.
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© 1981 D. Reidel Publishing Company
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Crain, B.R., Cobb, L. (1981). Parameter Estimation for Truncated Exponential Families. In: Taillie, C., Patil, G.P., Baldessari, B.A. (eds) Statistical Distributions in Scientific Work. NATO Advanced study Institutes Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8552-0_7
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DOI: https://doi.org/10.1007/978-94-009-8552-0_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-8554-4
Online ISBN: 978-94-009-8552-0
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