Penalized empirical likelihood function and it's application to generalized linear model

Maģistra darbā aplūkota vispārināto lineāro regresijas modeļu parametru novērtēšana ar soda funkciju un empīriskās ticamības metodēm. Ieviests soda funkcijas jēdziens un aplūkotas vairākas biežāk izmantotās soda funkcijas un to īpašības. Parādīta sodītās mazāko kvadrātu metodes novērtējumu labo īpašību, attiecībā pret nozīmīgo modeļa mainīgo atlasi, izpildīšanās simulētiem datiem. Definēts sodītās ticamības funkcijas jēdziens un aplūkots tās pielietojums vispārināto lineāro modeļu parametru novērtēšanā. Doti nepieciešamie algoritmi metodes praktiskai realizācijai. Sodītā empīriskā ticamības funkcija pielietota daudzdimensiju lineārās un loģistiskās regresijas datiem un secināts, ka metode labi darbojas parametru novērtēšanā, bet lai metode labi darbotos arī kā modeļa būtisko mainīgo atlasītājs, dotie algoritmi vēl jāpilnveido.Thesis outlines parameter estimation of generalized linear models with combination of penalty functions and empirical likelihood methods. Concept of penalty function was introduced together with definitions and properties of some frequently used penalty functions. It was shown that penalized least squares estimator has good properties useful for variable selection problems. Penalized empirical likelihood function was defined and it’s application to parameter estimation of generalized linear models was studied. Algorithms necessary for practical implementation of penalized empirical likelihood methods were given. It was concluded that penalized empirical likelihood algorithm presented in the thesis works satisfactory with respect to parameter estimation, while in order to use it as a tool for variable selection they need further inspection and development

Modelling insurance contracts duration with survival analysis methods

Darbā aplūkotas izdzīvošanas analīzes metodes. Tika apskatītas izdzīvošanas datu īpašības, Kaplana-Meiera izdzīvošanas funkcijas novērtējums, aplūkota Koksa proporcionālā modeļa uzbūve, tā parametru un izdzīvošanas funkcijas novērtēšanas metodoloģija, kā arī aplūkoti modeļa validācijas jautājumi. Metodes tika pielietotas apdrošināšanas līgumu darbības laika modelēšanai, izmantojot statistiskās paketes SPSS un R. Atslēgas vārdi: Izdzīvošanas analīze, Koksa proporcionālo risku modelis, Šonfelda atlikumi, martingala atlikumi, Koksa-Snella atlikumi.Diploma paper is dedicated to methods of survival analysis. Properties of survival data, Kaplan-Meier estimate of survival function, structure of Cox propoprtional hazards model and metodology for parameter and survival function estimation as well as model validation issues have been examined. Methods considered in the paper were applied to modelling duration of insurance agreements. using statistical software SPSS and R. Keywords: Survival analysis, Cox proportional hazards model, Schoenfeld residuals, mar- tingale residuals, Cox-Snell residual

Comparative Analysis of the Most Important Cardiovascular Risk Factors Based on Cross-Sectional Studies in the Population of Latvia

Background and Objectives: The aim of the study was to analyze the prevalence of cardiovascular risk factors (RFs) in Latvia from the population-based cross-sectional study performed in 2019–2020 and to compare the results with a similar study done in 2009–2010. Materials and Methods: The target sample of 6000 individuals representing a cross-section of Latvia’s inhabitants (aged 25–74) was formed using stratified two-stage cluster sampling. The survey had two components: (1) an interview using a pre-specified questionnaire and (2) physical examination (height, weight, arterial pressure) and collection of venous blood samples to measure levels of fasting glucose (Glu), total cholesterol (TC), high and low-density lipoprotein cholesterol (HDL-C/LDL-C), and triglycerides (Tg). In total, 4070 individuals were interviewed (32% non-response), from which 2218 (55%) individuals underwent physical examination and collection of blood samples. Results: The most frequently observed RFs were high LDL-C (62.0%), smoking (45.3%), and arterial hypertension (36.8%), while the prevalence of self-reported high cholesterol and hypertension was 19.3 and 18.6%, respectively. A decrease in the prevalence of hypertension, high LDL-C, and Glu was noted. Smoking decreased in younger men. The mean number of five most important cardiovascular RFs was 2.0 (95% confidence interval (CI) 2.0, 2.1); 2.3 (95% CI 2.2, 2.4) for men and 1.8 (95% CI 1.7, 19) for women. The average number of RFs has decreased by 0.3 in 10 years, t(5883) = −7.2, p Conclusions: Although the prevalence of cardiovascular RFs remains noteworthy, an improvement in the risk profile of the Latvian population has been observed over the past decade. The study shows subjective self-underestimation of cardiovascular risk