Three rates of convergence or separation via U-statistics in a dependent framework

Despite the ubiquity of U-statistics in modern Probability and Statistics, their non-asymptotic analysis in a dependent framework may have been overlooked. In a recent work, a new concentration inequality for U-statistics of order two for uniformly ergodic discrete time Markov chains has been proved. In this paper, we put this theoretical breakthrough into action by pushing further the current state of knowledge in three different active fields of research. First, we establish a new exponential inequality for the estimation of …

convergence framework statistics