Μοντέλα ακολουθιακής στατιστικής ανάλυσης και εφαρμογές
Sequential analysis models and applications
Στεφανίδης, Αλέξανδρος Λ.
KeywordsMartingales ; Χρόνοι στάσης ; Ακολουθιακή διαδικασία ; SPRT ; CUSUM ; Μέσο μήκος ροής ; Stopping times ; Sequential procedure ; Average run length
The purpose of this thesis is to review the basic methods of sequential analysis. In particular, we present the measure-theoretic approach for proving Wald’s equations and the fundamental equation, via the martingale theory and the theory of stopping times. We study the exact and asymptotic properties of the techniques for constructing fixed width confidence intervals for the mean of the normal distribution and their extension to p-dimensional confidence regions. A complete description of the sequential probability ratio test is given along with Wald’s approximation for estimating the operating characteristic function and the average sample number. Finally, applications of the sequential methodology are presented in order to define the analytical and geometric aspect of the cumulative sum statistical algorithm and the approximation of the average run length. The software package R was used for getting all the numerical results.