arXiv subjects
Publications and source records attributed to Lo Gane Samb.
In this note, we combine the two approaches of Billingsley (1998) and Csőrgő and Révész (1980), to provide a detailed sequential and descriptive for creating s standard Brownian motion, from a Brownian motion whose time space is the class of non-negative dyadic numbers. By adding the proof of Etemadi's inequality to text, it becomes self-readable and serves as an independent source for researches and professors.
A method of estimating the joint probability mass function of a pair of discrete random variables is described. This estimator is used to construct the conditional Shannon-Réyni-Tsallis entropies estimates. From there almost sure rates of convergence and asymptotic normality are established. The theorical results are validated by simulations.
We prove a uniform in bandwidth law of the iterated logarithm for the maximal deviation of kernel copula estimators from their expectations. We deal especially with the \textit{local linear}, the \textit{mirror-reflection} and the \textit{transformation} estimators. These results are useful for establishing the strong uniform in bandwidth consistency of these kernel estimators.