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Asymptotic Statistics
| Credits |
8 credit points |
| E-mail |
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| Aim |
An introduction to asymptotic methods in statistics. |
| Description |
The course starts with a review of various concepts of stochastic convergence (e.g. convergence in probability or in distribution), and properties of the multivariate normal distribution. Then the asymptotic properties of various statistical procedures are studied, including chi-square tests, moment estimators, M-estimators (including MLE), and kernel density estimators.
The examples are chosen according to importance in practical applications, and the theory is motivated by practical relevance, but the subjects are presented in theorem-proof form. The asymptotic optimality of these procedures, based on the "local asymptotic normality" of statistical models or Assouad's lemma, is not discussed during the course hours, but can be studied for extra credits (8 rather than 6). |
| Examination |
Written exam on the material of the lectures and problems sessions for 6 ECTS. Extension with 2 points to 8 ECTS through an oral exam on additional material. |
| Literature |
Lecture notes, and/or the book A.W. van der Vaart: Asymptotic Statistics (Cambridge University Press, 1998). |
| Prerequisites |
Undergraduate probability and statistics; measure theory is recommended.
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| Remarks |
See web site http://www.few.vu.nl/~geurt/mathstat.html; The course for 6 ECTS is identical to the course "Mathematical Statistics" in the bachelor program at the VU. |
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