Abstract
In this lecture we consider infinite-dimensional systems of estimating equations and show that solutions are asymptotically normal if the system is appropriately differentiable, extending the results on finite-dimensional Z- estimators to infinite dimensions. Next we show that this method can be applied to proving asymptotic normality of maximum likelihood estimators in semiparametric models, with as example, again, the Cox model.
Keywords
- Banach Space
- Score Function
- Maximum Likelihood Estimator
- Asymptotic Normality
- Information Matrix
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© 2002 Springer-Verlag Berlin Heidelberg
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(2002). Lecture: Infinite-dimensional Z-Estimators. In: Bernard, P. (eds) Lectures on Probability Theory and Statistics. Lecture Notes in Mathematics, vol 1781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47944-9_19
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DOI: https://doi.org/10.1007/3-540-47944-9_19
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43736-9
Online ISBN: 978-3-540-47944-4
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