Interval and Point Estimators for the Location Parameter of the Three-Parameter Lognormal Distribution

The three-parameter lognormal distribution is the extension of the two-parameter lognormal distribution to meet the need of the biological, sociological, and other fields. Numerous research papers have been published for the parameter estimation problems for the lognormal distributions. The inclusion of the location parameter brings in some technical difficulties for the parameter estimation problems, especially for the interval estimation. This paper proposes a method for constructing exact confidence intervals and exact upper confidence limits for the location parameter of the three-parameter lognormal distribution. The point estimation problem is discussed as well. The performance of the point estimator is compared with the maximum likelihood estimator, which is widely used in practice. Simulation result shows that the proposed method is less biased in estimating the location parameter. The large sample size case is discussed in the paper.

On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.

Comparison of Some Improved Estimators for Linear Regression Model under Different Conditions

Multiple linear regression model plays a key role in statistical inference and it has extensive applications in business, environmental, physical and social sciences. Multicollinearity has been a considerable problem in multiple regression analysis. When the regressor variables are multicollinear, it becomes difficult to make precise statistical inferences about the regression coefficients. There are some statistical methods that can be used, which are discussed in this thesis are ridge regression, Liu, two parameter biased and LASSO estimators. Firstly, an analytical comparison on the basis of risk was made among ridge, Liu and LASSO estimators under orthonormal regression model. I found that LASSO dominates least squares, ridge and Liu estimators over a significant portion of the parameter space for large dimension. Secondly, a simulation study was conducted to compare performance of ridge, Liu and two parameter biased estimator by their mean squared error criterion. I found that two parameter biased estimator performs better than its corresponding ridge regression estimator. Overall, Liu estimator performs better than both ridge and two parameter biased estimator.

Integrity-based kernel malware detection

Kernel-level malware is one of the most dangerous threats to the security of users on the Internet, so there is an urgent need for its detection. The most popular detection approach is misuse-based detection. However, it cannot catch up with today's advanced malware that increasingly apply polymorphism and obfuscation. In this thesis, we present our integrity-based detection for kernel-level malware, which does not rely on the specific features of malware. ^ We have developed an integrity analysis system that can derive and monitor integrity properties for commodity operating systems kernels. In our system, we focus on two classes of integrity properties: data invariants and integrity of Kernel Queue (KQ) requests. ^ We adopt static analysis for data invariant detection and overcome several technical challenges: field-sensitivity, array-sensitivity, and pointer analysis. We identify data invariants that are critical to system runtime integrity from Linux kernel 2.4.32 and Windows Research Kernel (WRK) with very low false positive rate and very low false negative rate. We then develop an Invariant Monitor to guard these data invariants against real-world malware. In our experiment, we are able to use Invariant Monitor to detect ten real-world Linux rootkits and nine real-world Windows malware and one synthetic Windows malware. ^ We leverage static and dynamic analysis of kernel and device drivers to learn the legitimate KQ requests. Based on the learned KQ requests, we build KQguard to protect KQs. At runtime, KQguard rejects all the unknown KQ requests that cannot be validated. We apply KQguard on WRK and Linux kernel, and extensive experimental evaluation shows that KQguard is efficient (up to 5.6% overhead) and effective (capable of achieving zero false positives against representative benign workloads after appropriate training and very low false negatives against 125 real-world malware and nine synthetic attacks). ^ In our system, Invariant Monitor and KQguard cooperate together to protect data invariants and KQs in the target kernel. By monitoring these integrity properties, we can detect malware by its violation of these integrity properties during execution.^

Optimal kernel development for real-time communications

The purpose of this research is to develop an optimal kernel which would be used in a real-time engineering and communications system. Since the application is a real-time system, relevant real-time issues are studied in conjunction with kernel related issues. The emphasis of the research is the development of a kernel which would not only adhere to the criteria of a real-time environment, namely determinism and performance, but also provide the flexibility and portability associated with non-real-time environments. The essence of the research is to study how the features found in non-real-time systems could be applied to the real-time system in order to generate an optimal kernel which would provide flexibility and architecture independence while maintaining the performance needed by most of the engineering applications. Traditionally, development of real-time kernels has been done using assembly language. By utilizing the powerful constructs of the C language, a real-time kernel was developed which addressed the goals of flexibility and portability while still meeting the real-time criteria. The implementation of the kernel is carried out using the powerful 68010/20/30/40 microprocessor based systems.

Integrity-Based Kernel Malware Detection

Kernel-level malware is one of the most dangerous threats to the security of users on the Internet, so there is an urgent need for its detection. The most popular detection approach is misuse-based detection. However, it cannot catch up with today's advanced malware that increasingly apply polymorphism and obfuscation. In this thesis, we present our integrity-based detection for kernel-level malware, which does not rely on the specific features of malware. We have developed an integrity analysis system that can derive and monitor integrity properties for commodity operating systems kernels. In our system, we focus on two classes of integrity properties: data invariants and integrity of Kernel Queue (KQ) requests. We adopt static analysis for data invariant detection and overcome several technical challenges: field-sensitivity, array-sensitivity, and pointer analysis. We identify data invariants that are critical to system runtime integrity from Linux kernel 2.4.32 and Windows Research Kernel (WRK) with very low false positive rate and very low false negative rate. We then develop an Invariant Monitor to guard these data invariants against real-world malware. In our experiment, we are able to use Invariant Monitor to detect ten real-world Linux rootkits and nine real-world Windows malware and one synthetic Windows malware. We leverage static and dynamic analysis of kernel and device drivers to learn the legitimate KQ requests. Based on the learned KQ requests, we build KQguard to protect KQs. At runtime, KQguard rejects all the unknown KQ requests that cannot be validated. We apply KQguard on WRK and Linux kernel, and extensive experimental evaluation shows that KQguard is efficient (up to 5.6% overhead) and effective (capable of achieving zero false positives against representative benign workloads after appropriate training and very low false negatives against 125 real-world malware and nine synthetic attacks). In our system, Invariant Monitor and KQguard cooperate together to protect data invariants and KQs in the target kernel. By monitoring these integrity properties, we can detect malware by its violation of these integrity properties during execution.

Sviluppo ed applicazione di tecniche di Multiple Kernel Learning per dati di neuroimaging

Questo lavoro di tesi riguarda lo studio e l’implementazione di un algoritmo di multiple kernel learning (MKL) per la classificazione e la regressione di dati di neuroimaging ed, in particolare, di grafi di connettività funzionale. Gli algoritmi di MKL impiegano una somma pesata di vari kernel (ovvero misure di similarità) e permettono di selezionare le features utili alla discriminazione delle istanze durante l’addestramento del classificatore/regressore stesso. L’aspetto innovativo introdotto in questa tesi è stato lo studio di un nuovo kernel tra grafi di connettività funzionale, con la particolare caratteristica di conservare l’informazione relativa all’importanza di ogni singola region of interest (ROI) ed impiegando la norma lp come metodo per l’aggiornamento dei pesi, al fine di ottenere soluzioni sparsificate. L’algoritmo è stato validato utilizzando mappe di connettività sintetiche ed è stato applicato ad un dataset formato da 32 pazienti affetti da deterioramento cognitivo lieve e malattia dei piccoli vasi, di cui 16 sottoposti a riabilitazione cognitiva tra un’esame di risonanza ma- gnetica funzionale di baseline e uno di follow-up. Le mappe di con- nettività sono state ottenute con il toolbox CONN. Il classificatore è riuscito a discriminare i due gruppi di pazienti in una configurazione leave-one-out annidata con un’accuratezza dell’87.5%. Questo lavoro di tesi è stato svolto durante un periodo di ricerca presso la School of Computer Science and Electronic Engineering dell’University of Essex (Colchester, UK).

CAUSAL INFERENCE WITH A CONTINUOUS TREATMENT AND OUTCOME: ALTERNATIVE ESTIMATORS FOR PARAMETRIC DOSE-RESPONSE FUNCTIONS WITH APPLICATIONS.

Causal inference with a continuous treatment is a relatively under-explored problem. In this dissertation, we adopt the potential outcomes framework. Potential outcomes are responses that would be seen for a unit under all possible treatments. In an observational study where the treatment is continuous, the potential outcomes are an uncountably infinite set indexed by treatment dose. We parameterize this unobservable set as a linear combination of a finite number of basis functions whose coefficients vary across units. This leads to new techniques for estimating the population average dose-response function (ADRF). Some techniques require a model for the treatment assignment given covariates, some require a model for predicting the potential outcomes from covariates, and some require both. We develop these techniques using a framework of estimating functions, compare them to existing methods for continuous treatments, and simulate their performance in a population where the ADRF is linear and the models for the treatment and/or outcomes may be misspecified. We also extend the comparisons to a data set of lottery winners in Massachusetts. Next, we describe the methods and functions in the R package causaldrf using data from the National Medical Expenditure Survey (NMES) and Infant Health and Development Program (IHDP) as examples. Additionally, we analyze the National Growth and Health Study (NGHS) data set and deal with the issue of missing data. Lastly, we discuss future research goals and possible extensions.

Bahadur representation of linear kernel quantile estimator of VaR under mixing assumptions

Bahadur representation and its applications have attracted a large number of publications and presentations on a wide variety of problems. Mixing dependency is weak enough to describe the dependent structure of random variables, including observations in time series and longitudinal studies. This note proves the Bahadur representation of sample quantiles for strongly mixing random variables (including ½-mixing and Á-mixing) under very weak mixing coe±cients. As application, the asymptotic normality is derived. These results greatly improves those recently reported in literature.

Diseño e implementación del kernel de xDEVS, versión distribuida

Para entender nuestro proyecto, debemos comprender DEVS. Dentro de los formalismos más populares de representación de sistemas de eventos discretos se encuentra DES. En la década de los 70, el matemático Bernard Zeigler propuso un formalismo general para la representación de dichos sistemas. Este formalismo denominado DEVS (Discrete EVent System Specification) es el formalismo más general para el tratamiento de DES. DEVS permite representar todos aquellos sistemas cuyo comportamiento pueda describirse mediante una secuencia de eventos discretos. Estos eventos se caracterizan por un tiempo base en el que solo un número de eventos finitos puede ocurrir. DEVS Modelado y Simulación tiene múltiples implementaciones en varios lenguajes de programación como por ejemplo en Java, C# o C++. Pero surge la necesidad de implementar una plataforma distribuida estable para proporcionar la mecánica de interoperabilidad e integrar modelos DEVS diversificados. En este proyecto, se nos dará como código base el core de xDEVS en java, aplicado de forma secuencial y paralelizada. Nuestro trabajo será implementar el core de manera distribuida de tal forma que se pueda dividir un sistema DEVS en diversas máquinas. Para esto hemos utilizado sockets de java para hacer la transmisión de datos lo más eficiente posible. En un principio deberemos especificar el número de máquinas que se conectarán al servidor. Una vez estas se hayan conectado se les enviará el trabajo específico que deberán simular. Cabe destacar que hay dos formas de dividir un sistema DEVS las cuales están implementadas en nuestro proyecto. La primera es dividirlo en módulos atómicos los cuales son subsistemas indivisibles en un sistema DEVS. Y la segunda es dividir las funciones de todos los subsistemas en grupos y repartirlos entre las máquinas. En resumen el funcionamiento de nuestro sistema distribuido será comenzar ejecutando el trabajo asignado al primer cliente, una vez finalizado actualizará la información del servidor y este mandara la orden al siguiente y así sucesivamente.

RATE OF CONVERGENCE OF MAXIMUM LIKELIHOOD ESTIMATORS UNDER RELAXED SMOOTHNESS CONDITIONS ON THE LIKELIHOOD FUNCTION

This report reviews literature on the rate of convergence of maximum likelihood estimators and establishes a Central Limit Theorem, which yields an O(1/sqrt(n)) rate of convergence of the maximum likelihood estimator under somewhat relaxed smoothness conditions. These conditions include the existence of a one-sided derivative in θ of the pdf, compared to up to three that are classically required. A verification through simulation is included in the end of the report.