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On the identifiability of measurement error in the bifurcating autoregressive model

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  • Huggins, Richard

Abstract

Huggins and Staudte (1994) considered a mixed linear model for the analysis of cell lineage data and in models for the covariance structure which involved measurement error, it was not immediately clear that the parameters involved were identifiable. Whilst a numerical examination of the Hessian matrix at the estimated parameter values gave some reassurance, this was not theoretically satisfying. Here a matrix formulation of the robust estimating functions of Huggins (1993a, b) as applied in Huggins and Staudte (1994), which include the maximum likelihood estimating functions under the assumption of multivariate normality as a special case, is given along with a direct proof linking identifiability expressed in terms of the estimating functions with the information matrix or its analogue in more general settings. The resulting conditions on the estimating functions may then be checked globally using computer algebra, suggesting a method for establishing identifiability in mixed linear models in general.

Suggested Citation

  • Huggins, Richard, 1996. "On the identifiability of measurement error in the bifurcating autoregressive model," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 17-23, March.
    • Handle: RePEc:eee:stapro:v:27:y:1996:i:1:p:17-23
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    References listed on IDEAS

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    1. Crowder, Martin, 1986. "On Consistency and Inconsistency of Estimating Equations," Econometric Theory, Cambridge University Press, vol. 2(3), pages 305-330, December.
    2. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
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    Cited by:

    1. Terpstra, Jeff T. & Elbayoumi, Tamer, 2012. "A law of large numbers result for a bifurcating process with an infinite moving average representation," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 123-129.

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