Pseudo-Maximum Likelihood and Lie Groups of Linear Transformations

Gouriéroux, Christian and Monfort, Alain and Zakoian, Jean-Michel (2017): Pseudo-Maximum Likelihood and Lie Groups of Linear Transformations.

Abstract

Newey, Steigerwald (1997) considered a univariate conditionally heteroscedastic model, with independent and identically distributed errors. They showed that the parameters characterizing the serial dependence are consistently estimated by any pseudo maximum likelihood approach, whenever two additional parameters, one for location, one for scale, are appropriately introduced in the model. Our paper extends their result to a more general multivariate framework. We show the consistency of any pseudo maximum likelihood method for multivariate models based on Lie groups of (linear, affine) transformations when these groups commute, or at least satisfy a property of closure under commutation. We explain how to introduce appropriately the additional parameters which capture all the bias due to the misspecification of the error distribution. We also derive the asymptotic distribution of the PML estimators.

• Item Type: MPRA Paper
• Language: English
• Keywords: Pseudo Maximum Likelihood, Lie Group, Transformation Model, GARCH Model, Infinitesimal Generator, Rotation, Computer Vision, Machine Learning, Volatility Matrices.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation

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