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March, 1983 On the Estimation of the Parameters of Markov Probability Models Using Macro Data
Adriaan P. Van Der Plas
Ann. Statist. 11(1): 78-85 (March, 1983). DOI: 10.1214/aos/1176346058

Abstract

In this paper we consider the problem of estimating the parameters of a Markov model using so-called macro data. It will be shown that the stochastic process of the macro data is a Markov chain, which uniquely determines the probability structure of the underlying Markov model. A conditional least squares estimator exists under very weak conditions and this estimator is strongly consistent as time tends to infinity. Moreover this estimator is shown to be asymptotically normal under some additional assumptions.

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Adriaan P. Van Der Plas. "On the Estimation of the Parameters of Markov Probability Models Using Macro Data." Ann. Statist. 11 (1) 78 - 85, March, 1983. https://doi.org/10.1214/aos/1176346058

Information

Published: March, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0508.62072
MathSciNet: MR684865
Digital Object Identifier: 10.1214/aos/1176346058

Subjects:
Primary: 60J10
Secondary: 62F10 , 62M05

Keywords: a.s. convergence , a.s. uniform convergence , asymptotic normality , grouped chain , least squares estimator , macro data , Markov models

Rights: Copyright © 1983 Institute of Mathematical Statistics

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Vol.11 • No. 1 • March, 1983
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