This work examines the problem of sequential change detection in the constant drift of a Brownian motion in the case of multiple alternatives. As a performance measure an extended Lorden’s criterion is proposed. When the possible drifts, assumed after the change, have the same sign, the CUSUM rule designed to detect the smallest in absolute value drift, is proven to be the optimum. If the drift...

Assuming that sensors have full local memory, we introduce a novel test for the problem of decentralized change detection that is asymptotically optimum. According to our proposed scheme, sensors perform locally repeated SPRTs and communicate, asynchronously, their one-bit decisions to a fusion center. The fusion center in turn uses the sequentially acquired information to perform a CUSUM test ...

We consider the problem of detecting a proportional change in the intensity of a counting process with a continuous compensator. We prove that if the counting process does not have explosions, the CUSUM test is optimal in a Lorden sense. In particular, the CUSUM test minimizes the worst-case conditional expected number of events that occur after the change and before raising an alarm given the ...

A control chart is one of the tools Statistical Process Control (SPC) used to monitor a production process. The charts ability detect data that crosses border often done using variable transformation. In this paper, we will introduce cumulative sum (CUSUM) based on Link Relative transformation technique regression approach. results showed with was more sensitive compared previous CUSUM and char...

Kupershmidt and Tuenter have introduced reflection symmetries for the q-Bernoulli numbers and the Bernoulli polynomials in 2005 , 2001 , respectively. However, they have not dealt with congruence properties for these numbers entirely. Kupershmidt gave a quantization of the reflection symmetry for the classical Bernoulli polynomials. Tuenter derived a symmetry of power sum polynomials and the cl...

In this paper, we consider the problem of testing for parameter changes in time series models based on a cusum test. Although the test procedure is well established for the mean and variance in time series models, a general parameter case has not been discussed in the literature. Therefore, here we develop a cusum test for parameter change in a more general framework. As an example, we consider...

A New Look at the Stopping Times Related to the Trading Strategies Vilen Abramov We provide a probabilistic framework by which an analytic analysis can be performed for the trading strategies under various continuous price dynamics. This, in part, is done by making a connection to the cumulative sum (cusum) procedure of quality control. Although the cusum procedure has been studied quiet extens...

Abstract: This paper considers the problem of testing for parameter change in random coefficient integer-valued autoregressive models. To overcome some size distortions of the existing estimate-based cumulative sum (CUSUM) test, we suggest estimating function-based test and residual-based CUSUM test. More specifically, we employ the estimating function of the conditional least squares estimator...