Asymptotics of Bernstein estimators on the simplex, part 2. The boundary case

In this paper, we study the asymptotic properties (bias, variance, mean squared error) of Bernstein estimators for cumulative distribution functions and density functions near the boundary of the $d$-dimensional simplex. The results generalize those found in Leblanc (2012), who treated the case $d=1$, and complement the results from Ouimet (2020) in the interior of the simplex. Different parts of the boundary having different dimensions makes the analysis more complex.