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The information matrix test for Gaussian mixtures

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Abstract

In incomplete data models the EM principle implies the moments the Information Matrix test assesses are the expectation given the observations of the moments it would assess were the underlying components observed. This principle also leads to interpretable expressions for their asymptotic covariance matrix adjusted for sampling variability in the parameter estimators under correct specification. Monte Carlo simulations for finite Gaussian mixtures indicate that the parametric bootstrap provides reliable finite sample sizes and good power against various misspecification alternatives. We confirm that 3-component Gaussian mixtures accurately describe cross-sectional distributions of per capita income in the 1960-2000 Penn World Tables.

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  • Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2024. "The information matrix test for Gaussian mixtures," Working Papers wp2024_2401, CEMFI.
    • Handle: RePEc:cmf:wpaper:wp2024_2401
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    More about this item

    Keywords

    Expectation-Maximisation principle; incomplete data; Hessian matrix; outer product of the score.;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

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