We answer a 15-year-old open question about the exact upper bound for bivariate copulas with a given diagonal section by giving an explicit formula for this bound. As an application, we determine the maximal asymmetry of bivariate copulas with a given diagonal section and construct a copula that attains it. We derive a formula for the maximal asymm...
Copulas are mathematical tools for modeling the dependence between the components of a random vector. They are frequently used in fields such as finance, economics, and risk management. Chapter 1 and 2 of this thesis provide a review of the main results in the study of copulas including their basic properties, estimation methods, the empirical copu...
We determine the upper and lower bounds for possible values of Kendall's tau of a bivariate copula given that the value of its Spearman's footrule or Gini's gamma is known, and show that these bounds are always attained.
In this thesis, we review some applications of random matrix theory in machine learning and theoretical deep learning. More specifically, we review data modelling in the regime of numerous and large dimensional data, a method for estimating covariance matrix distances in the aforementioned regime, as well as an asymptotic analysis of a simple neura...
Published in Applied Mathematics and Nonlinear Sciences
To revise the Chinese version of Planned Happenstance Career Inventory (PHCI), a total of 1161 college students were recruited in the study, among whom 327 were used for item analysis and exploratory factor analysis (EFA), 568 for further confirmatory factor analysis (CFA) and internal consistency reliability analysis, and 266 were retested after a...
Developments in computer vision has sought to design deep neural networks which trained on a large set of images are able to generate high quality artificial images which share semantic qualities with the original image set. A pivotal shift was made with the introduction of the generative adversarial network (GAN) by Goodfellow et al.. Building on ...
This paper examines the impact of several macroeconomic variables on property prices in Sweden. Linear regression is used to construct severalmathematical models relating the macroeconomic variables to property prices. Using methods of variables selection and goodness of fit measures,two final models are selected and subsequently compared, resultin...
Statistical power is an important topic taught in most graduate-level and undergraduate-level mathematical statistics courses, but it is often difficult to understand conceptually. Visualizing the power curve, sampling distributions, and how they interact can help students more easily conceptualize power, but the creation of such visuals can be dif...
Egon Vielrose was an outstanding Polish demographer, statistician and econometrician. He studied mathematics at Warsaw University and economics at the Higher School of Trade and then he qualified as an assistant professor at Warsaw University. His research interests focused on problems of demography, mathematical statistics, econometrics and socio‑...
Convolutional artificial neural networks can be applied for image-based object classification to inform automated actions, such as handling of objects on a production line. The present thesis describes theoretical background for creating a classifier and explores the effects of introducing a set of relatively recent techniques to an existing ensemb...
