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<div>Networks and point processes provide flexible tools for representing and modeling complex dependencies in data arising from various social and physical domains. Graphs, or networks, encode relational dependencies between entities, while point processes characterize temporal or spatial interactions among events.</div><div><br></div><div>In the first part of this dissertation, we consider dynamic network data (such as communication networks) in which links connecting pairs of nodes appear continuously over time. We propose latent space point process models to capture two different aspects of the data: (i) communication occurs at a higher rate between individuals with similar latent attributes (i.e., homophily); and (ii) individuals tend to reciprocate communications from others, but in a varied manner. Our framework marries ideas from point process models, including Poisson and Hawkes processes, with ideas from latent space models of static networks. We evaluate our models on several real-world datasets and show that a dual latent space model, which accounts for heterogeneity in both homophily and reciprocity, significantly improves performance in various link prediction and network embedding tasks.</div><div><br></div><div>In the second part of this dissertation, we develop nonparametric goodness-of-fit tests for discrete distributions and point processes that contain intractable normalization constants, providing the first generally applicable and computationally feasible approaches under those circumstances. Specifically, we propose and characterize Stein operators for discrete distributions, and construct a general Stein operator for point processes using the Papangelou conditional intensity function. Based on the proposed Stein operators, we establish kernelized Stein discrepancy measures for discrete distributions and point processes, which enable us to develop nonparametric goodness-of-fit tests for un-normalized density/intensity functions. We apply the kernelized Stein discrepancy tests to discrete distributions (including network models) as well as temporal and spatial point processes. Our experiments demonstrate that the proposed tests typically outperform two-sample tests based on the maximum mean discrepancy, which, unlike our goodness-of-fit tests, assume the availability of exact samples from the null model.</div><div><br></div>

The accelerated lifetime model is considered. To test the influence of the covariate we transform the model in a regression model. Since censoring is allowed this approach leads to a goodness-of-fit problem for regression functions under censoring. So nonparametric estimation of regression functions under censoring is investigated, a limit theorem for a L2-distance is stated and a test procedure is formulated. Finally a Monte Carlo procedure is proposed.

Diploma thesis abstract Thesis title: Statistical inference in multivariate distributions based on copula models Author: Vojtěch Kika This diploma thesis aims for statistical inference in copula based models. Ba- sics of copula theory are described, followed by methods for statistical inference. These are divided into three main groups. First of them are parametric methods for copula parameter estimation which assume fully parametric structure, thus for both joint and marginal distributions. The second group consists of semi- parametric methods for copula parameter estimation which, unlike parametric methods, do not require parametric structure for marginal distributions. The last group describes goodness-of-fit tests used for testing the hypothesis that consi- dered copula belongs to some specific copula family. The thesis is accompanied by a simulation study that investigates the dependence of the observed coverage of the asymptotic confidence intervals for copula parameter on the sample size. Pseudolikelihood method was chosen for the simulation study since it is one of the most popular semiparametric methods. It is shown that sample size of 50 seems to be sufficient for the observed coverage to be close to the theoretical one. For Frank and Gumbel-Hougaard copula families even sample size of 30 gives us...

Introduction: Non-compliance with respiratory protection programs among firefighters may put them at increased risk of injury and illness from occupational exposures during fire extinguishing activities. This research aims to characterize respiratory protection practices among Florida firefighters. This information will allow better understanding of factors that are associated with non-compliance with respiratory protection guidelines. Methods: Survey questionnaire was used to characterize Florida fire departments in this cross sectional study. Four hundred and seventy-seven surveys were administered to Florida firefighters both in person and electronically to collect information regarding firefighter knowledge and participation in their respective respiratory protection programs during the past twelve months. Survey questions were developed from the model set by the National Fire Protection Association which provides standards and regulations regarding firefighter protections. Collected data were used to produce summary statistics regarding firefighter department size, coverage area, and firefighter employment type. Further data analysis used Statistical Analysis Software to compute multinomial logistic regression analysis. Results: The 477 respondents were 91% male with a mean age 39 years old (range 21-65 years). The majority of respondents, 76%, were non-smokers, 21% former smokers, and 3% current smokers. In regards to ethnicity, respondents were 77% Caucasian, 13% Hispanic, 3% African-American, and 4% other. Most respondents were career firefighters, 97%, with less than ten years of experience, 44%, working in a fire department with at least 21 firefighters, 98%. Most respondents, 80%, had a written respiratory program in place. The most cited reason for not having implemented a written respiratory program was lack of knowledge related to the program. Multinomial logistic regression analysis of departments with response areas of at least 250,000 square miles produced a statistically significant 0.44 odds ratio for having a written respiratory program as compared to those with a less than 10,000 square miles response area. Conclusion: Additional resources need to be given to Florida fire departments to ensure that all firefighters receive adequate respiratory protection in accordance with National Fire Protection Association guidelines. There is an association between fire departments with large response areas and non-compliance with respiratory protection guidelines in regards to: having a written respiratory program, the frequency of respiratory fit testing, and the frequency of medical fitness testing. This suggests that rural fire departments need additional resources to ensure fire fighters are adequately protected. Additional research should focus on why these differences exist in the rural fire departments. Respondents stating a lack of knowledge or no requirement for a written respiratory program suggest that future efforts should focus on respiratory protection education and training.

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In this thesis we introduce, implement and compare several multivariate goodness-of-fit tests. First of all, we will focus on universal mul- tivariate tests that do not place any assumptions on parametric families of null distributions. Thereafter, we will be concerned with testing of multi- variate normality and, by using Monte Carlo simulations, we will compare power of five different tests of bivariate normality against several alternati- ves. Then we describe multivariate skew-normal distribution and propose a new test of multivariate skew-normality based on empirical moment genera- ting functions. In the final analysis, we compare its power with other tests of multivariate skew-normality. 1