Local asymptotic theory for multiple solutions of likelihood equations, with application to a single ion channel model.

Robin Milne, B.R. Clarke, G.F. Yeo

    Research output: Contribution to journalArticle

    Abstract

    This paper investigates local asymptotic theory when there are multiple solutions of the likelihood equations due to non-identifiability arising as a consequence of incomplete information. Local asymptotic results extend in a stochastic way the notion of a Frechet expansion, which is then used to prove asymptotic normality of the maximum likelihood estimator under certain conditions. The local theory, which provides simultaneous consistency and asymptotic normality results, is applied to a bivariate exponential model exhibiting non-identifiability. This statistical model arises as an approximation to the distribution of observable sojourn-times in the states of a two-state Markov model of a single ion channel and the non-identifiability is a consequence of an inability to record sojourns less than some small detection limit. For each of two possible estimates, confidence intervals are constructed using the asymptotic theory. Although it is not possible to decide between the two estimates on the basis of a single realization, an appropriate solution of the likelihood equations may be found using the additional information contained in data based on two different detection limits; this is investigated numerically and by simulation.
    Original languageEnglish
    Pages (from-to)133-146
    JournalScandinavian Journal of Statistics
    Issue number20
    Publication statusPublished - 1993

    Fingerprint

    Ion Channels
    Channel Model
    Multiple Solutions
    Asymptotic Theory
    Likelihood
    Detection Limit
    Asymptotic Normality
    Bivariate Exponential
    Sojourn Time
    Exponential Model
    Incomplete Information
    Maximum Likelihood Estimator
    Estimate
    Markov Model
    Statistical Model
    Confidence interval
    Approximation
    Asymptotic theory
    Simulation
    Asymptotic normality

    Cite this

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    title = "Local asymptotic theory for multiple solutions of likelihood equations, with application to a single ion channel model.",
    abstract = "This paper investigates local asymptotic theory when there are multiple solutions of the likelihood equations due to non-identifiability arising as a consequence of incomplete information. Local asymptotic results extend in a stochastic way the notion of a Frechet expansion, which is then used to prove asymptotic normality of the maximum likelihood estimator under certain conditions. The local theory, which provides simultaneous consistency and asymptotic normality results, is applied to a bivariate exponential model exhibiting non-identifiability. This statistical model arises as an approximation to the distribution of observable sojourn-times in the states of a two-state Markov model of a single ion channel and the non-identifiability is a consequence of an inability to record sojourns less than some small detection limit. For each of two possible estimates, confidence intervals are constructed using the asymptotic theory. Although it is not possible to decide between the two estimates on the basis of a single realization, an appropriate solution of the likelihood equations may be found using the additional information contained in data based on two different detection limits; this is investigated numerically and by simulation.",
    author = "Robin Milne and B.R. Clarke and G.F. Yeo",
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    language = "English",
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    Local asymptotic theory for multiple solutions of likelihood equations, with application to a single ion channel model. / Milne, Robin; Clarke, B.R.; Yeo, G.F.

    In: Scandinavian Journal of Statistics, No. 20, 1993, p. 133-146.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Local asymptotic theory for multiple solutions of likelihood equations, with application to a single ion channel model.

    AU - Milne, Robin

    AU - Clarke, B.R.

    AU - Yeo, G.F.

    PY - 1993

    Y1 - 1993

    N2 - This paper investigates local asymptotic theory when there are multiple solutions of the likelihood equations due to non-identifiability arising as a consequence of incomplete information. Local asymptotic results extend in a stochastic way the notion of a Frechet expansion, which is then used to prove asymptotic normality of the maximum likelihood estimator under certain conditions. The local theory, which provides simultaneous consistency and asymptotic normality results, is applied to a bivariate exponential model exhibiting non-identifiability. This statistical model arises as an approximation to the distribution of observable sojourn-times in the states of a two-state Markov model of a single ion channel and the non-identifiability is a consequence of an inability to record sojourns less than some small detection limit. For each of two possible estimates, confidence intervals are constructed using the asymptotic theory. Although it is not possible to decide between the two estimates on the basis of a single realization, an appropriate solution of the likelihood equations may be found using the additional information contained in data based on two different detection limits; this is investigated numerically and by simulation.

    AB - This paper investigates local asymptotic theory when there are multiple solutions of the likelihood equations due to non-identifiability arising as a consequence of incomplete information. Local asymptotic results extend in a stochastic way the notion of a Frechet expansion, which is then used to prove asymptotic normality of the maximum likelihood estimator under certain conditions. The local theory, which provides simultaneous consistency and asymptotic normality results, is applied to a bivariate exponential model exhibiting non-identifiability. This statistical model arises as an approximation to the distribution of observable sojourn-times in the states of a two-state Markov model of a single ion channel and the non-identifiability is a consequence of an inability to record sojourns less than some small detection limit. For each of two possible estimates, confidence intervals are constructed using the asymptotic theory. Although it is not possible to decide between the two estimates on the basis of a single realization, an appropriate solution of the likelihood equations may be found using the additional information contained in data based on two different detection limits; this is investigated numerically and by simulation.

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