Simulation-Based Bias Correction Methods for Complex Models

Stéphane Guerrier, Elise Dupuis-Lozeron, Yanyuan Ma, Maria Pia Victoria-Feser

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Along with the ever increasing data size and model complexity, an important challenge frequently encountered in constructing new estimators or in implementing a classical one such as the maximum likelihood estimator, is the computational aspect of the estimation procedure. To carry out estimation, approximate methods such as pseudo-likelihood functions or approximated estimating equations are increasingly used in practice as these methods are typically easier to implement numerically although they can lead to inconsistent and/or biased estimators. In this context, we extend and provide refinements on the known bias correction properties of two simulation-based methods, respectively, indirect inference and bootstrap, each with two alternatives. These results allow one to build a framework defining simulation-based estimators that can be implemented for complex models. Indeed, based on a biased or even inconsistent estimator, several simulation-based methods can be used to define new estimators that are both consistent and with reduced finite sample bias. This framework includes the classical method of the indirect inference for bias correction without requiring specification of an auxiliary model. We demonstrate the equivalence between one version of the indirect inference and the iterative bootstrap, both correct sample biases up to the order n − 3 . The iterative method can be thought of as a computationally efficient algorithm to solve the optimization problem of the indirect inference. Our results provide different tools to correct the asymptotic as well as finite sample biases of estimators and give insight on which method should be applied for the problem at hand. The usefulness of the proposed approach is illustrated with the estimation of robust income distributions and generalized linear latent variable models. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)146-157
Number of pages12
JournalJournal of the American Statistical Association
Volume114
Issue number525
DOIs
StatePublished - Jan 2 2019

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Bias Correction
Indirect Inference
Estimator
Simulation
Inconsistent
Bootstrap
Biased
Model
Income Distribution
Pseudo-likelihood
Latent Variable Models
Model Complexity
Estimating Equation
Likelihood Function
Maximum Likelihood Estimator
Bias correction
Linear Model
Refinement
Efficient Algorithms
Equivalence

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Guerrier, Stéphane ; Dupuis-Lozeron, Elise ; Ma, Yanyuan ; Victoria-Feser, Maria Pia. / Simulation-Based Bias Correction Methods for Complex Models. In: Journal of the American Statistical Association. 2019 ; Vol. 114, No. 525. pp. 146-157.
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Simulation-Based Bias Correction Methods for Complex Models. / Guerrier, Stéphane; Dupuis-Lozeron, Elise; Ma, Yanyuan; Victoria-Feser, Maria Pia.

In: Journal of the American Statistical Association, Vol. 114, No. 525, 02.01.2019, p. 146-157.

Research output: Contribution to journalArticle

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