Finance and Stochastics

, Volume 14, Issue 4, pp 569–591 | Cite as

A global consistency result for the two-dimensional Pareto distribution in the presence of misspecified inflation

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Abstract

A global consistency result for the ML estimator of a misspecified two-parameter Pareto distribution is proved. The misspecification is due to the assumption of a wrong inflation rate, which violates the i.i.d. assumption in the model. We also investigate how far away from the true parameters one finds the ML estimator of the misspecified model (asymptotically for a small misspecification r). Finally, for the case where the misspecification depends on the number of observations n, i.e., r=rn, and where \(r_{n}\stackrel{n\to \infty}{\longrightarrow}0\), we prove a central limit theorem for the ML estimator.

Keywords

ML estimation Global consistency Pareto distribution Misspecified model Inflation 

Mathematics Subject Classification (2000)

62F12 91B70 

JEL Classification

C60 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Institute for Mathematical Methods in Economics, Financial and Actuarial MathematicsVienna University of TechnologyViennaAustria
  2. 2.Edgeworth Centre for Financial MathematicsUniversity College CorkCorkIreland

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