Pós-Graduação em Estatística Asymptotics for Empirical Processes associated to a Regenerative Sequence
Marta Lizeth Calvache (MAT/UnB)
In this webinar, we will present some results about the asymptotic behavior of the partial sums of a regenerative sequence $\{X_n\}{n\geqslant 0}$. We will prove that $S_n =\sum_{j=1}^{n} \varphi(X_j )$, with $\varphi$ a measurable function, converges in Mallows distance to a Gaussian random variable. As a direct application, we will establish the weak convergence of a special type of partial sum, the empirical process, as well as its inverse process, the empirical quantile process. And, as by product of this weak convergence, we will obtain the asymptotic null distribution for a regenerative sample of the statistics such as Kolmogorov-Smirnov, Cramer-von Mises and some statistics based on the 2nd-order Mallows distance.
05-Oct-2020 (Thursday), 2:00 pm (Brasília time)