The Annals of Statistics

On the Estimation of the Parameters of Markov Probability Models Using Macro Data

Adriaan P. Van Der Plas

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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.

Article information

Source
Ann. Statist., Volume 11, Number 1 (1983), 78-85.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346058

Digital Object Identifier
doi:10.1214/aos/1176346058

Mathematical Reviews number (MathSciNet)
MR684865

Zentralblatt MATH identifier
0508.62072

JSTOR
links.jstor.org

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 62F10: Point estimation 62M05: Markov processes: estimation

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

Citation

Plas, Adriaan P. Van Der. On the Estimation of the Parameters of Markov Probability Models Using Macro Data. Ann. Statist. 11 (1983), no. 1, 78--85. doi:10.1214/aos/1176346058. https://projecteuclid.org/euclid.aos/1176346058


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