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Zhang, Qi; Wang, Kai-Ping; Li, De-Li; Lin, Lu

GMM and misspecification correction for misspecified models with diverging number of parameters. (English) Zbl 1452.62212

Acta Math. Appl. Sin., Engl. Ser. 35, No. 4, 780-797 (2019).
This paper considers statistical estimation by the generalized method of moments (GMM) when the model is misspecified. Focusing on the situation where the numbers of parameters and predictors tend to infinity as the sample size grows, the authors prove local and global consistency to and asymptotic normality around the solution to the estimation equation, what they call the pseudoparameter vector. Then the authors propose a semiparametric method to correct the misspecification and show its asymptotic properties. Although the numerical experiments with a simple regression model demonstrate the effectiveness of the correction method, they are a little too limited to verify the asymptotic properties.
Reviewer: Kazuho Watanabe (Toyohashi)

Cited in 1 Document

MSC:

62F10 Point estimation
62F12 Asymptotic properties of parametric estimators
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference

Keywords:

misspecified model; high dimensionality; generalized method of moments (GMM); misspecification correction

Software:

Excel
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Full Text: DOI

References:

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