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Statistical Inference with Local Optima

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  • Yen-Chi Chen

Abstract

We study the statistical properties of an estimator derived by applying a gradient ascent method with multiple initializations to a multi-modal likelihood function. We derive the population quantity that is the target of this estimator and study the properties of confidence intervals (CIs) constructed from asymptotic normality and the bootstrap approach. In particular, we analyze the coverage deficiency due to finite number of random initializations. We also investigate the CIs by inverting the likelihood ratio test, the score test, and the Wald test, and we show that the resulting CIs may be very different. We propose a two-sample test procedure even when the maximum likelihood estimator is intractable. In addition, we analyze the performance of the EM algorithm under random initializations and derive the coverage of a CI with a finite number of initializations. Supplementary materials for this article are available online.

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  • Yen-Chi Chen, 2023. "Statistical Inference with Local Optima," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(543), pages 1940-1952, July.
    • Handle: RePEc:taf:jnlasa:v:118:y:2023:i:543:p:1940-1952
    DOI: 10.1080/01621459.2021.2023550
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    Cited by:

    1. Zachary Porreca, 2024. "A Note on Uncertainty Quantification for Maximum Likelihood Parameters Estimated with Heuristic Based Optimization Algorithms," Papers 2401.07176, arXiv.org.

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