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Estimating Fisher Information Matrix in Latent Variable Models

Abstract : The Fisher information matrix (FIM) plays a key role in statistics. It is crucial in practice not only for evaluating the precision of parameter estimations, but also for example in statistical testing, for experimental designs or in post model selection inference. In latent variable models, the evaluation of the FIM is non-elementary due to the presence of unobserved variables. Therefore the observed FIM is usually considered. When it can not be evaluated analytically, several methods have been proposed to estimate it. Among the most frequently used approaches are Monte-Carlo methods or iterative algorithms derived from the missing information principle. These methods however focus on the moment estimate of minus the expectation of the Hessian matrix of the log-likelihood. Therefore they require to compute second derivatives of the log-likelihood which is not always possible and has some disadvantages from a computational point of view. In this work we consider the estimate of the FIM equal to the moment estimate of the covariance matrix of the score. It only requires to compute first derivatives of the log-likelihood. We derive a stochastic approximation algorithm for computing this estimator when its expression is not explicit. We study the asymptotic properties of the proposed estimator and of the corresponding stochastic approximation algorithm. Some numerical experiments are performed in mixed-effects models and mixture models to illustrate the finite sample size properties of the estimators and of the algorithm. We also fit a pharmacokinetic real dataset of Theophylline using a nonlinear mixed effects model and evaluate both FIM estimates.
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https://hal.inrae.fr/hal-02790629
Contributor : Migration Prodinra <>
Submitted on : Friday, June 5, 2020 - 6:40:38 AM
Last modification on : Saturday, May 1, 2021 - 3:47:56 AM

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  • HAL Id : hal-02790629, version 1
  • PRODINRA : 410321

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Estelle Kuhn, Maud Delattre. Estimating Fisher Information Matrix in Latent Variable Models. [Technical Report] 2017. ⟨hal-02790629⟩

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