On a Problem of Statistical Inference in Null Recurrent Diffusions |
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Authors: | R Höpfner Yu Kutoyants |
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Institution: | (1) Johannes Gutenberg Universität Mainz, D-55099 Mainz, Germany;(2) Laboratoire Statistique et Processus, Université du Maine, F-72085 Le Mans Cedex 09, France |
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Abstract: | We consider a particular example of statistical inference in null recurrent one-dimensional diffusions. In a first parametric model, we prove local asymptotic mixed normality (LAMN) and efficiency of the sequence of maximum likelihood estimates (MLE): its speed of convergence is n
/2 with ranging over (0, 1). In a second semiparametric model (where in addition an unknown nuisance function with known compact support is included in the drift), we prove a local asymptotic minimax bound and specify asymptotically efficient estimates for the unknown parameter. |
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Keywords: | diffusions null recurrence limit theorems parametric inference semiparametric model LAMN convolution theorem local asymptotic minimax bound |
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