https://www.um.edu.mt/library/oar/handle/123456789/30457 Tue, 07 Apr 2026 13:52:47 GMT 2026-04-07T13:52:47Z https://www.um.edu.mt/library/oar/handle/123456789/93463 Title: Analyzing longitudinal count data related to re-sits in the faculty of science using GLMs and hierarchical poisson random coefficient models Abstract: The GLM family subsumes a large number of statistical models that are widely used in practical applications for prediction purposes. GLMs overcome the limitations of traditional Regression models, which assume a Normal distribution for the responses. In this thesis, we present three GLMs to forecast the number of ECTS resits for students in the Faculty of Science. The first model is a Normal regression model that is plagued by model misspecifications. The second and third models improve the model fit by assuming a Poisson and Gamma distribution that respectively lead to the logarithmic and reciprocal canonical link functions. Three predictors were identified that were thought to contribute considerably in explaining the variability in the responses. These include the University entry qualification score, the subjects studied and the year in which the ECTS resit count was recorded. A limitation of GLMs is that they assume independence for the responses. It is very implausible that responses from longitudinal data are independent. An approach that overcomes this limitation is based on considering the hierarchical structure of the study design. Multilevel models, also known as random coefficient models, focus on nested sources of variability and involve measurements of variables for more than one level of hierarchy. Our data set comprise responses (number of ECTS resits) that are nested within the students (level-2 units) and students that are nested within departments (level 3 units). The data is appropriate for multilevel modelling. In this dissertation, we present four multilevel models to forecast the number of ECTS resits for B.Sc.(Hons.) students. These include a random intercept and a random coefficient model each with two and three levels of nesting. Description: B.SC.(HONS)STATS.&OP.RESEARCH Sun, 01 Jan 2017 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/93463 2017-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/72988 Title: Nonparametric density estimation concerning social benefits in Malta Abstract: Nonparametric density estimation involves obtaining an estimate for the unknown probability density function given a sample of size 𝑛 but without having any prior knowledge on the form of the function. We shall consider the wavelet and kernel density estimation methods to obtain the estimate of the unknown density function. Since this density function is unknown, we shall work in an infinite dimensional space. However, in practice we are not able to work in this space, thus we shall use the method of sieves to approximate our infinite dimensional space with a sequence of finite dimensional spaces. We shall use wavelets as our orthonormal bases which will then be used to obtain the required wavelet density estimator. On the other hand, the kernel density estimator is based on the choice on the smoothing parameter and the kernel function. We shall compare the two nonparmateric methods by applying both techniques to a sample of Maltese individuals who were entitled to receive different types of social benefits. Description: B.SC.(HONS)STATS.&OP.RESEARCH Sun, 01 Jan 2017 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/72988 2017-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/72977 Title: An overview of ROC analysis Abstract: The Receiver Operating Characteristic (ROC) curve is considered to be one of the best developed statistical tools to analyze the performance of binary classifier systems, such as medical diagnostic tests, and to classify elements of a population into two groups, namely “diseased” and “healthy”. In this dissertation, the theoretical construct of the ROC curve is studied, along with summary measures derived from the ROC curve, particularly the Area under the Curve (AUC). Different techniques from three estimation frameworks, namely the non-parametric, parametric and semi-parametric frameworks, are discussed, and their performance is compared using simulation studies. The best estimation techniques, according to the simulation studies, are then applied to two real medical datasets, obtained from Mater Dei hospital. Methodology on how an optimal threshold value is derived from the ROC curve is discussed, and is then used to determine the best threshold for both applications. Description: B.SC.(HONS)STATS.&OP.RESEARCH Sun, 01 Jan 2017 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/72977 2017-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/72975 Title: Testing efficiency of football betting markets using adaptive drift models Abstract: Over the years, the efficiency of financial markets has been studied extensively in literature, and the interest for investigating notions of efficiency also in the context of sports betting markets has been growing considerably. In its semi-strong form, the efficient market hypothesis holds the concept that a market is efficient if it fully reflects all publicly available information and has the ability to efficiently adapt to new information. Under efficiency, betting strategies based on this information should not be able to generate significant profits and consistent winning patterns. In this study, betting strategies informed by goal difference forecasts obtained from adaptive drift models are used to investigate the efficiency of Asian handicap betting markets for German football games. Findings based on predictions for the 2015/16 and 2016/17 Bundesliga seasons for FC Bayern Munich games suggest that efficiency and the efficient market hypothesis are supported. However, applying similar methodologies for 1. FSV Mainz 05 yields substantial winnings and indicates that inefficiency may be detected among various bookmakers. Description: B.SC.(HONS)STATS.&OP.RESEARCH Sun, 01 Jan 2017 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/72975 2017-01-01T00:00:00Z