Nicholas Katada graduated as Dux from Turramurra High School in 2011 and was awarded the HSC Premier’s Award for All Round Excellence. In 2012 Nicholas commenced his Bachelor of Science (Advanced Mathematics). His first year studies included the Special Studies Program for gifted mathematics students and the Talented Student Program. In 2013 Nicholas was placed on the Sydney University Dean’s list in recognition of outstanding academic achievement and he was the recipient of the Dean’s Scholarship for Science.
Nicholas is currently a third year undergraduate student majoring in Mathematics and Statistics at the University of Sydney. His areas of interest include real analysis, probability theory, and statistics. His research scholarship for AMSI will examine the leave one out likelihood estimator for the location parameter of unbounded densities, in the context of discrete sampling of the variance Gamma Levy process.
Optimal Convergence Rate of Leave-One-Out Likelihood Estimation for the Location Parameter of Unbounded Densities
We investigate the so-called “leave-one-out” likelihood estimation of the location parameter for a density that is unbounded at the mode. In particular, we take a close look at discrete sampling of the variance gamma Levy process for the two cases; the equidistant observation time stepsize (i) is very small but constant (low-frequency sampling), and (ii) converges to zero as the number of observations tends to infinity (high-frequency sampling). This project requires strong familiarity with real analysis and measure theory.