sequential testing point process renewal theory

#Sequential testing point process renewal theory pdf

We show that the proposed tests have asymptotic power one. Which yields the threshold to control the asymptotic type-I-error. Proposed procedures we provide the limit distribution under the null hypothesis An analogue of Wald’s Fundamental Identity is. Good for early changes while being advantageous for later changes. The properties of a sequential probability ratio test to decide on the parameter values of a stationary autoregressive process are investigated. Monitoring period into account, we also consider a modified moving-sum-versionĪs well as a version of a Page-monitoring scheme. theories of sequential testing and sequential change-point detection. Unlike the originally proposed scheme that takes all observations of the to the sequential sampling inspection procedures of Dodge and Romig (1929), to. Sequential change-point detection when the distribution parameters are unknown is a fundamental problem in statistics and machine learning. Take different observations into account to make a decision at a given time Within this framework, we consider several monitoring schemes that $U$-statistics which contains as an example a sequential CUSUM test based onĭifferences in mean but also includes a robust sequential Wilcoxon change point

#Sequential testing point process renewal theory pdf

The reason for considering both the theories together is that the models usually proposed for both the theories - input distribution for dam theory, and lifedistribution for renewal theory - are similar, and only a slight modification (to account for the ‘release rules’ in dam theory, plus the fact that we have two barriers) is necessary to derive results in dam theory from those of renewal theory.Download a PDF of the paper titled Sequential change point tests based on U-statistics, by Claudia Kirch and Christina Stoehr Download PDF Abstract: We propose a general framework of sequential testing procedures based on It is the purpose of this paper to show how a generalization of the Fundamental Identity to Markovian variables, (Phatarfod ) can be used to derive approximate results in some problems in dam and renewal theories where the random variables involved have Markovian dependence. Phatarfod used it for a problem in dam theory. Bartlett used it for the gambler's ruin problem and also for a simple renewal problem. Renewal theory and its applications Limit Theorems Example 7.9 Example 7.9 Consider the renewal process whose inter-arrival distribution is the convolution of two exponentials that is, F F 1 F 2, where F i(t) 1 e it, i 1 2. It is well known that Wald's Fundamental Identity (F.I.) in sequential analysis can be used to derive approximate (and, sometimes exact) results in most situations wherein we have essentially a random walk phenomenon. The detection mechanism as well as the input design techniques are extended to the multihypothesis case. Both o²ine and online generated signals are considered. Campbells formula in the theory of point processes (see Theorem 106 in. In designing inputs to improve the performance of the CUSUM test the design objectives are taken as not only to minimize the average detection delay but also to ensure a specified false alarm rate. where Tn is the time of the nth renewal (general renewal processes are studied. The application of SPRT to the change detection problem is discussed and the properties of an associated cumulative sum (CUSUM) test are analyzed. The Fundamental Identity of sequential analysis and the performance measures of the test are derived for the case of autoregressive models. The sequential probability ratio test (SPRT) which arises as a suboptimal test within this framework is investigated in detail.

It is shown that some important properties of the decision rules related to the classical case still hold. This work is concerned with the detection and diagnosis of abrupt changes in the dynamics of single input single output stochastic systems and the design of auxiliary inputs for this purpose.įirst, the problem is put in a decision theoretic framework and the concepts of classical decision theory (where no input is available to the decision maker) are augmented to accommodate the input design as well as the decision rules for change detection.