Rates of convergence for classes of functions: The non-i.i.d. case

Let Xi, i >= 1, be a sequence of [phi]-mixing random variables with values in a sample space (X, A). Let L(Xi) = P(i) for all i >= 1 and let n, n >= 1, be classes of real-valued measurable functions on (X, A). Given any function g on (X, A), let Sn(g) = [Sigma]i = 1n {g(Xi) - Eg(Xi)}. Under weak metric entropy conditions on n and under growth conditions on both the mixing coefficients and the maximal variance V := V(n) := maxi[phi]-mixing random variables metric entropy chaining techniques Ottaviani maximal inequality blocking techniques