Moving frames to test for change-points. Sequential and best tests (Q2847904)

The standard procedure for estimating a parameter or to test some hypothesis concerning a parameter is to take a sample and perform the necessary analysis. The first obvious (polemic?) remark against this procedure is that one might have taken an unnecessarily large sample; a smaller one would have been sufficient, and this would also, on occasions, have saved lives. Alternatively, the sample was not large enough in order to allow for a significant conclusion.NEWLINENEWLINE A natural suggestion thus would be to perform a sequential procedure. This means that one observes the process at hand at increasing time points and takes actions as soon as something ``special'' occurs, that is, by stopping when something particular occurs. One particular such situation is when one wishes to detect a change in the process, that is, to detect a change-point. The same problem again, one wishes only to detect a change when there is one, thus avoiding false alarms.NEWLINENEWLINE This is the background for the thesis under review. The model that is investigated is an asymptotic regression model, this is the subject of part II, which follows part I in which the model is introduced in a non-sequential setting, together with a backwards operator, with the aid of which the author, i.a., can express certain known results in a more efficient way.NEWLINENEWLINE Throughout main focus is on the Winer process and variations of it. Another point is that such procedures often are based on ``windows'' that is, increments of the process (rather than on the cumulative process). On point of discussion is the size of the window, which, recalling our introduction should be neither too short nor too long.NEWLINENEWLINE In the second part some sequential procedures are introduced and properties of various stopping time procedures are compared via simulations. Part III investigates the problems further, and part IV contains various proofs and details.