Large Deviation, Statistical Inference and Probability Theory

Denise Uwamariya is Assistant Lecturer at the University of Rwanda (UR), College of Science and Technology (CST) at the Department of Mathematics since in 2013 where she started as Tutorial Assistant in 2010. In 2016, she worked as volunteer/Internal Statistician at National Institute of Statistics of Rwanda (NISR). From 2018, Denise is a PhD student in mathematical statistics at Linköping University in Sweden. 

Denise has a strong background in mathematics and statistics. She holds a Bachelor's degree of science in Applied Mathematics, Statistics Option from (UR), (CST) former Kigali Institute of Science and Technology (KIST) in Rwanda, and a Master's degree in Technomathematics with major subject in Data Driven Modeling and minor subject in Business Administration from Lappeenranta University of Technology (LUT) in Finland. 

In addition to this, she is a member of the Rwanda Association of Women in Science and Engineering (RAWISE), and the Organization for Women in Science for the Developing World (OWSD). 

Her interest includes to use different types of data for decision making, research and to become the best Statistician.

Current Positions

  • Assistant Lecturer, University of Rwanda
  • PhD student, Linköping University

Expertise

Mathematics and Statistics.

Research Focus

Large Deviation, Statistical inference and Probability theory.

Research Topic

Large deviation, the normalized empirical spectral density and anti-eigenvalues

Let X be p x n random matrix with i.i.d entries where p is population dimension and n is a sample size.

The most classical statistical methods are available in case of n>p. This means that most of the classical limit theorems are derived under the assumption that the dimension p is fixed, and the sample size n goes to infinity which implies that in high dimensional data classical statistical methods designed for the low dimensional case either perform poorly or are no longer applicable in high dimensional settings. Therefore; new classical technique methods are needed for the case where n and p both goes to infinity. The contribution of the research is to study the large deviation probability of random matrix Xp x n when p is fixed, and n goes to infinity as whereas when both goes to infinity for the case where the entries xij for i=1,⋯, p and j=1,⋯,n are standard normal and for general case together with anti-eigenvalues which has many applications in statistical inference.

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