Abstract
We consider moment based estimation methods for estimating parameters of the negative binomial distribution that are almost as efficient as maximum likelihood estimation and far superior to the celebrated zero term method and the standard method of moments estimator. Maximum likelihood estimators are difficult to compute for dependent samples such as samples generated from the negative binomial first-order autoregressive integer-valued processes. The power method of estimation is suggested as an alternative to maximum likelihood estimation for such samples and a comparison is made of the asymptotic normalized variance between the power method, method of moments and zero term method estimators.
Similar content being viewed by others
References
Al-Osh MA, Alzaid AA (1987) First-order integer-valued autoregressive (INAR(1)) process. J Time Ser Anal, 8(3):261–275
Anscombe FJ (1950) Sampling theory of the negative binomial and logarithmic series distributions. Biometrika 37:358–382
Brockwell PJ, Davis RA (2002) Introduction to time series and forecasting 2nd edn. Springer, New York
Ehrenberg ASC (1988) Repeat-Buying: Facts, theory and applications. Charles Griffin & Company Ltd., London,
Fisher RA (1941) The negative binomial distribution. Ann Eugenics 11:182–187
Haldane JBS (1941) The fitting of binomial distributions. Ann Eugenics 11:179–181
Johnson NL, Kotz S, Kemp AW (1992) Univariate discrete distributions. 2nd edn Wiley, New York
McKenzie E (1986) Autoregressive moving-average processes with negative-binomial and geometric marginal distributions. Adv Appl Prob 18(3):679–705
McKenzie E (1988) Some ARMA models for dependent sequences of Poisson counts. Adv Appl Prob 20(4):822–835
Savani V, Zhigljavsky A (2006) Efficient estimation of parameters of the negative binomial distribution. Commun Stat Theory Methods 35(5):1–17
Serfling RJ (1980) Approximation theorems of mathematical statistics. Wiley, New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Savani, V., Zhigljavsky, A.A. Efficient parameter estimation for independent and INAR(1) negative binomial samples. Metrika 65, 207–225 (2007). https://doi.org/10.1007/s00184-006-0071-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-006-0071-x