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Abramov, VilenStopping Times Related to Trading Strategies
PHD, Kent State University, 2008, College of Arts and Sciences / Department of Mathematical Science

We use CUSUM procedure to analyze trading the line strategy. Closed form expressions concerning probabilistic characteristics of the CUSUM stopping time and stopped process were obtained in discrete time setting for a wide class of processes. This class of discrete processes was recently defined by K. M. Khan and R. A. Khan.

In continuous time, the CUSUM procedure applied to the processes driven by a particular stochastic differential equation was studied. As a result the joint Laplace transform of the maximum process and CUSUM stopping time was derived.

Finally, the trading the line strategy was studied for the process driven by the fractional Brownian motion. As in regular Brownian motion case, the Laplace transform was linked to the partial differential equation. Although the lack of optional sampling theorem in this case prevents us from getting a closed form expression, the structure of the Laplace transform is derived. By using these results we point some of the subtle features of the trading the line strategy.

Committee:

Kazim Khan (Committee Chair); Sergey Anokhin (Committee Member); Hassan Allouba (Committee Member); Oana Mocioalca (Committee Member); Doug Delahanty (Committee Co-Chair)

Subjects:

Mathematics

Keywords:

Stochastic Process; CUSUM Stopping Time; Brownian Motion; fractional Brownian Motion; Laplace Transform; Stochastic Differential Equation; Trading the Line Strategy

Hongcheng, LiMultivariate Extensions of CUSUM Procedure
PHD, Kent State University, 2007, College of Arts and Sciences / Department of Mathematical Science
In quality control, to use the recent history data of the process, Page(1954) introduced the CUSUMprocedure in the univariate case. It has been proved(Moustakides,1986)that (when the process is out of control) the CUSUMprocedure has the smallest expected run length among all procedures with the same in-control ARL. In this dissertation, we investigate the multivariate extension of Page's CUSUMprocedure. The expectation and the variance of the run length for various multivariate distributions are studied. Both analytical and simulation results of the ARLand variance are given. The exact expression for the ARLof a trinomial model for any decision intervals are given. Computer programs computing the ARLand variance for any given decision intervals are also given.

Committee:

Mohammad Khan (Advisor)

Subjects:

Mathematics

Keywords:

ARL; CUSUM; quality control; trinomial model; variance

Jokinen, Jeremy D.Determination of Change in Online Monitoring of Longitudinal Data: An Evaluation of Methodologies
Doctor of Philosophy (PhD), Ohio University, 2015, Experimental Psychology (Arts and Sciences)
Longitudinal data collection is becoming increasingly common with the increased use of internet-based/technologically-based methods for data capture. In fields as diverse as healthcare, engineering, fisheries management, political science, economics, and psychology, often analyses are conducted to determine if some change to the pattern of incoming data has occurred. If a change has occurred analysis should make that determination as quickly as possible. A data-pattern change is critical information, as it may indicate a change in the health status of patients, changing political attitudes, or, as in the case of the proposed study, changes to the safety profile of consumer products. The methods to analyze these longitudinal databases for indicators of change are as varied as the fields collecting the data. To date, no single study has examined the varied methodologies to determine the relative accuracy of the methods and no study has attempted to determine the relative duration over which accurate change determinations are made. This study examined the performance of these methodologies across three sets of simulated data as well as a single, large-scale safety database for a major consumer healthcare company. The simulated data is comprised of random noise data streams and data streams with actual changes in data pattern (signals). The three simulated data sets differ by the strength of the signal. The consumer safety database is comprised of call center data (n>725,000 records) from consumers who call to report a side effect (adverse event) while taking a company product. Healthcare professionals flag products identified as having a confirmed safety signal. Analyses were conducted retrospectively to determine if this change in safety status could have been detected by the statistical methods examined in this study for 30 days prior to the date of the confirmed signal. For each of the three simulated data sets and the actual product safety database, mean and 95% CI for sensitivity and specificity as well as AUC ROC over time line graphs were used to examine differences between statistical methodologies. Results of analysis the simulated data set and the actual data set indicated the modified control chart method performed well throughout the 31-day time period of analysis. Modified control charting performed significantly better than other methods, proving to be a useful change detection method more than 20 days prior to the confirmed safety signal. Though RCI, Bayesian, and CUSUM did not perform as well as modified control charting, they did perform significantly better than all other methods. The computational simplicity of RCI makes this method worth considering for broad applications.

Committee:

Bruce Carlson, PhD (Committee Chair)

Subjects:

Quantitative Psychology

Keywords:

Change detection; CUSUM; Bayesian; online data monitoring

WANG, BODetecting shift in mean and variance for both uncorrelated and correlated series using several popular tests
Master of Arts, Miami University, 2014, Economics
Recently there has been a keen interest in the statistical analysis of change point detection. This is because change point problems can be encountered in many fields such as economics, finance, medicine and so on. In this project, we firstly provide a comprehensive review of several popular tests in detecting mean and variance shift. To investigate the performance of those tests, Type I error and power are examined followed by two empirical investigations. Our results show that for mean shift detection, both K&L test and ARMA residual test work well for normal distributed process; for ARMA process, the ARMA residual test is the best; for variance shift detection, change in mean has huge influence on Type I error estimation and I&T test is more powerful than K&L test for GARCH process.

Committee:

Thomas Fisher, PhD (Advisor); Li Jing, PhD (Committee Member); Davis George, PhD (Committee Member)

Subjects:

Economics

Keywords:

CUSUM; changepoints; ARMA series; shift in mean; shift in variance

Crowe, Edward R.A strategy for the synthesis of real-time statistical process control within the framework of a knowledge based controller
Doctor of Philosophy (PhD), Ohio University, 1995, Chemical Engineering (Engineering)

Artificial intelligence is a broad field of computer-based technologies designed to emulate the cognitive abilities demonstrated in human behavior. These emerging technologies are being investigated for a wide variety of applications. Statistical process control, conversely, is a classical technique used in process monitoring to detect abnormal variation of key parameters. This research proposes a strategy to integrate these technologies into an intelligent control system that can detect an extrinsic disturbance, identify the cause, and adjust its control parameters to compensate for a drift in product quality.

This control strategy, applied to a continuous distillation process, provides two distinct feedback control schemes. The primary feedback control structure is based on fuzzy logic. The auxiliary feedback scheme, based on the integrated technologies of neural networks, expert system, and statistical process control, is designed to detect and compensate for assignable causes that normally require human intervention. These disturbances are automatically identified and the control parameters modified to compensate for their effects.

Two objectives were achieved in this study. First, the performance of fuzzy logic control was evaluated in comparison to conventional PID control. Second, the dynamic pattern recognition capability of a neural network was demonstrated by imposing disturbances on the process. This was realized through the integration of process data conditioned by a CUSUM charting technique. This data was then used as the input vector to a backpropagation neural network. The cause of the disturbance was identified by the embedded neural network trained off-line to recognize certain disturbance patterns. A set of IF-THEN rules was used to validate the disturbance classification.

The results of this research clearly show promise for further integration of these technologies. Fuzzy logic exhibited excellent control characteristics for both set point and load changes. The neural network, with the CUSUM interface, correctly identified each extrinsic disturbance and initiated an algorithm to regulate the product quality within established control limits.

Committee:

W. Chen (Advisor)

Subjects:

Engineering, Chemical

Keywords:

synthesis; real-time statistical process control; based controller; extrinsic disturbance; PID control; backpropagation neural network; CUSUM charting technique

Al-Mafrachi, Basheer Husham AliDetection of DDoS Attacks against the SDN Controller using Statistical Approaches
Master of Science in Computer Engineering (MSCE), Wright State University, 2017, Computer Engineering
In traditional networks, switches and routers are very expensive, complex, and inflexible because forwarding and handling of packets are in the same device. However, Software Defined Networking (SDN) makes networks design more flexible, cheaper, and programmable because it separates the control plane from the data plane. SDN gives administrators of networks more flexibility to handle the whole network by using one device which is the controller. Unfortunately, SDN faces a lot of security problems that may severely affect the network operations if not properly addressed. Threat vectors may target main components of SDN such as the control plane, the data plane, and/or the application. Threats may also target the communication among these components. Among the threats that can cause significant damages include attacks on the control plane and communication between the controller and other networks components by exploiting the vulnerabilities in the controller or communication protocols. Controllers of SDN and their communications may be subjected to different types of attacks. DDoS attacks on the SDN controller can bring the network down. In this thesis, we have studied various form of DDoS attacks against the controller of SDN. We conducted a comparative study of a set of methods for detecting DDoS attacks on the SDN controller and identifying compromised switch interfaces. These methods are sequential probability ratio test (SPRT), count-based detection (CD), percentage-based detection (PD), and entropy-based detection (ED). We implemented the detection methods and evaluated the performance of the methods using publicly available DARPA datasets. Finally, we found that SPRT is the only one that has the highest accuracy and F score and detect almost all DDoS attacks without producing false positive and false negative.

Committee:

Bin Wang, Ph.D. (Advisor); Yong Pei, Ph.D. (Committee Member); Mateen Rizki, Ph.D. (Committee Member)

Subjects:

Computer Engineering

Keywords:

SDN; Controller; DDoS attacks; SPRT; CD; PD; CUSUM; ED

Hoblos, JalaaSelfish Node Misbehaving Statistical Detection with Active MAC Layer NAV Attack in Wireless Networks}
MS, Kent State University, 2006, College of Arts and Sciences / Department of Computer Science
In wireless networks such as IEEE 802.11, all nodes contending to access the medium are supposed to follow the rules of the Medium Access Control (MAC) layer. As the number of nodes increases; the probability of collisions increases (often exponentially) causing longer backoff values for the contending nodes. Selfish nodes (or misbehaving nodes) tempt to manipulate their backoff parameters to gain more access to the channel, and hence higher performance than their fair share. In this thesis, we discuss the problem of misbehaving traffic sources in the context of IEEE 802.11 MAC layer in which one or more nodes aggressively allocate more bandwidth than their fair share. We implement several statistical control detection techniques often used in industries, and propose three new methods to monitor and detect the misbehaving traffic sources. The statistical methods include Control Charts such as EWMA, and CuSum, and methods based on Hypothesis Testing and Confidence Intervals. We named our proposed methods the Mean Deviation algorithm (MeDev), the Percentage Test (PeT), and the Cumulative Deviation algorithm (CuDev). We evaluate the performance of all the methods through simulation models and statistical analysis to test their effectiveness. We use multiple parameters as basis for comparison between the implemented methods. These parameters include the Average Run Length (ARL), the Hit Ratio (HR), the False Positives (F+), and the Complexity (the processing time, the data storage, and the dependency on historic data). The results show that our proposed algorithm CuDev outperforms all other implemented methods. CuDev is able to detect selfish sources with a very high HR (often 1), a very low F+ (no more than 1%), and a very short ARL. Further, we study CuDev in the context of distributed and centralized autonomous systems. Our results indicate that one can get the same performance with less than 10% monitoring time. This is particularly important in a distributed system where power consumption is a big concern. It is also essential in a centralized system where constant monitoring of a large number of sources by the Base Station (BS) alone may become quickly a big burden on it. We later confirm CuDev' behavior in both environments using mathematical modeling and analysis.

Committee:

Hassan Peyravi (Advisor)

Subjects:

Computer Science

Keywords:

MISBEHAVING; CuDev; CuSum; ARL; HTDM; MeDev; EWMA