Consider a linear regression model y₁ = x₁β + u₁, where the u₁'S afe weakly dependent random variables, the x₁'s are known design nonrandom variables, and β is an unknown parameter. We define an M-estimator β_n of) β corresponding to a smooth score function. Then, the second-order Edgeworth...

Asymptotic normality is established for a class of statistics which includes as special cases weighted sum of independent and identically distributed (i.i.d.) random variables, unsigned linear rank statistics, signed rank statistics, linear combination of functions of order statistics, and...

In this note, we establish the convergence properties for a broad class of random variables of the form Sn = [integral operator]Fn(Tn - s)[nu]n(ds) where Tn is some random variable, Fn is an empirical distribution function based on an independent sample of size n, and [nu]n is some measure.