Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1991. / Vita. Abstract. Includes bibliographical references (leaves 218-221). Also available via the Internet

In the last few years, telemetric data arising from embedded vehicle sensors brung an overwhelming abundance of information to companies. There is no indication that this will be abated in future. This information concerning driving behaviour brings an opportunity to carry out analysis. The merging of telemetric data and informatics gives rise to a sub-field of data science known as telematics. This work encompasses matrix variate and kernel density methods for the purposes of analysing telemetric data. These methods expand the current literature by alleviating the issues that arise with high-dimensional data. / Thesis / Master of Science (MSc)

An error in the Gaussian random variate generator by Kinderman and Ramage is described that results in the generation of random variates with an incorrect distribution. An additional statement that corrects the original algorithm is given. / Series: Preprint Series / Department of Applied Statistics and Data Processing

Matrix variate distributions present a innate way to model random matrices. Realiza- tions of random matrices are created by concurrently observing variables in different locations or at different time points. We use a finite mixture model composed of matrix variate normal densities to cluster matrix variate data. The matrix variate data was generated by accelerometers worn by children in a clinical study conducted at McMaster. Their acceleration along the three planes of motion over the course of seven days, forms their matrix variate data. We use the resulting clusters to verify existing group membership labels derived from a test of motor-skills proficiency used to assess the children’s locomotion. / Thesis / Master of Science (MSc)

Clustering and classification is the process of finding underlying group structure in heterogenous data. With the rise of the “big data” phenomenon, more complex data structures have made it so traditional clustering methods are oftentimes not advisable or feasible. This thesis presents methodology for analyzing three different examples of these more complex data types. The first is three-way (matrix variate) data, or data that come in the form of matrices. A large emphasis is placed on clustering skewed three-way data, and high dimensional three-way data. The second is click- stream data, which considers a user’s internet search patterns. Finally, co-clustering methodology is discussed for very high-dimensional two-way (multivariate) data. Parameter estimation for all these methods is based on the expectation maximization (EM) algorithm. Both simulated and real data are used for illustration. / Thesis / Doctor of Philosophy (PhD)

Let (X1, X2, X3) be a tri-variate normal vector with a non-singular co-variance matrix ∑ , where for i ≠ j, ∑ij < 0 . It is shown here that it is then possible to determine the three means, the three variances and the three correlation coefficients based only on the knowledge of the probability density function for the minimum variate Y = min{X1 , X2 , X3 }. We will present a method for identifying the nine parameters which consists of careful determination of the asymptotic orders of various bivariate tail probabilities.

The enterprise finance crisis forecast could provide alarm to managers and investors of the enterprise, many scholars advised different alarm models to explain and predict the enterprise is facing finance crisis or not. These models can be classified into three categories by analysis method, the first is single-variate model, it¡¦s easy to implement. The second is multi-variate model which need to fit some statistical assumption, and the third is Artificial Neural Network model which doesn¡¦t need to fit any statistical assumption. However, these models do not consider the industrial effect, different industry could have different finance crisis pattern. This study uses the advantage of Artificial Neural Network to build the process of the enterprise finance crisis forecast model, because it doesn¡¦t need to fit any statistical assumption. Finally, the study use reality finance data to prove the process, and compare with the other models. The result shows the model issued by this study is suitable in Taiwan Electronic Industry, but the performance in Taiwan architecture industry is not better than other models.

<p>Asian options are an important family of derivative contracts with a wide variety of applications in commodity, currency, energy, interest rate, equity and insurance markets. In this master's thesis, we investigate methods for evaluating the price of the Asian call options with a fixed strike. One of them is the Monte Carlo method. The accurancy of this method can be observed through variance of the price. We will see that the variance with using Monte Carlo method has to be decreased. The Variance Reduction technique is useful for this aim. We will give evidence of the efficiency of one of the Variance Reduction thechniques - Control Variate method - in a mathematical context and a numerical comparison with the ordinary Monte Carlo method.</p>

Asian options are an important family of derivative contracts with a wide variety of applications in commodity, currency, energy, interest rate, equity and insurance markets. In this master's thesis, we investigate methods for evaluating the price of the Asian call options with a fixed strike. One of them is the Monte Carlo method. The accurancy of this method can be observed through variance of the price. We will see that the variance with using Monte Carlo method has to be decreased. The Variance Reduction technique is useful for this aim. We will give evidence of the efficiency of one of the Variance Reduction thechniques - Control Variate method - in a mathematical context and a numerical comparison with the ordinary Monte Carlo method.

The transformed rejection method uses inversion to sample from the dominating density of a rejection algorithm. But in contrast to the usual method it is enough to know the inverse distribution function F^(-1)(x) of the dominating density. This idea can be applied to various continuous (e.g. normal, Cauchy and exponential) and discrete (e.g. binomial and Poisson) distributions with high acceptance probabilities. The resulting algorithms are short, simple and fast. Even more important is the fact that the quality of the method when used in combination with a linear congruential uniform generator is high compared with the quality of the ratio of uniforms method. In addition transformed rejection can be easily employed for correlation induction. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing