Επί μεθόδων στατιστικής συπερασματολογίας με χρήση της εμπειρικής χαρακτηριστικής συνάρτησης

The subject of the present dissertation is the analytic and numerical investigation of certain procedures of Statistical Inference which use the empirical characteristic function (ecf). In Chapter I we introduce the characteristic function and the ecf and go through some of their important properties. We then provide an intoduction to the history of the applications of the ecf in Statistical Inference and a quick description of the original material in this dissertation which is included in Chapters II to IV. Chapter II contains an analytic and numerical investigation of the behavior of an estimator in which the polar coordinates of the ecf are calculated at a finite number of points. Asymptotic normality is proved and the efficiency of the proposed estimator is investigated based on asymptotic results and results from finite samples. These results pertain to some well known symmetric models which are useful in applied research and for which the standard methods of estimation are not efficient. In chapter III an adaptive estimator of the median of symmetric populations is introduced. In the proposed method of estimation a tail-weight index is used based on the modulus of the ecf for the specification of the points where the argument of the same function is to be calculated to yield the estimate. The estimator has an asymptotic normal distribution and high asymptotic efficiency. A simulation study reveals the efficiency properties of the estimator in small samples from a wide range of symmetric models. The estimators studied in the second chapter are employed to construct a goodness-of-fit test based on a test statistic which is introduced in Chapter IV. The asymptotic chi-square distribution of the test statistic is derived in the general case and in the case of symmetric populations. In this case the test statistic is decomposed into two statistics which are asymptotically independent and appropriate the first for testing shape and the second for testing symmetry of the distribution. The proposed method conveniently applies to the case of testing for symmetric stability for which a power study is presented with small samples from distributions frequently occuring in applied research. Finally in the Conclusions the results contained in the present dissertation are discussed and some proposals for future study are made.

Grantor dc:publisher

University of Patras

Year dc:date

1990

Authors dc:creator

• Meintanis, Simos
• Μεϊντάνης, Σίμος

• Έλεγχοι καλής προσαρμογής
• Εμπειρική χαρακτηριστική συνάρτηση
• Μη παραμετρική εκτίμηση
• Παραμετρική εκτίμηση
• Χαρακτηριστική συνάρτηση
• Characteristic function
• Empirical characteristic function
• Goodness of fit tests
• Non-parametric estimation
• Φυσικές Επιστήμες
• Μαθηματικά
• Natural Sciences
• Mathematics

Language dc:language

gre

Identifier

10.12681/eadd/1494

OAI identifier oai:identifier

oai:10442/1494