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September, 1976 A Note on the Estimation of Parameters in a Bernoulli Model with Dependence
Jay L. Devore
Ann. Statist. 4(5): 990-992 (September, 1976). DOI: 10.1214/aos/1176343597


A generalization of a Bernoulli process which incorporates a dependence structure was given by Klotz (1972, 1973), in which he considered $X_1, X_2, \cdots, X_n$ as a stationary two-state Markov chain with state space $\{0, 1\}$. The parameters of the process are $p = P(X_i = 1)$ and $\lambda$, which measures the degree of persistence in the chain. Klotz was unable to solve the equations arising from the full likelihood for the M.L.E.'s of $p$ and $\lambda$, so proposed and investigated an ad hoc procedure. Here explicit solutions are obtained for M.L.E.'s based on a modified likelihood function, where the modification consists of neglecting the first term of the full likelihood. In addition it is observed that Klotz's equations can in fact be solved explicitly.


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Jay L. Devore. "A Note on the Estimation of Parameters in a Bernoulli Model with Dependence." Ann. Statist. 4 (5) 990 - 992, September, 1976.


Published: September, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0349.62053
MathSciNet: MR418373
Digital Object Identifier: 10.1214/aos/1176343597

Primary: 62M05
Secondary: 62F10

Keywords: dependent Bernoulli sequence , Markov chain , maximum likelihood estimation

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 5 • September, 1976
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