In this paper we derive almost sure representation theorems and limit distribution results for the solution of a general parametric equation of integral type evaluated at the empirical distribution function. In particular, these are applied to R-, L- and (scale invariant) M-estimates as well as...

Let Xn1, ..., Xnn be an array of independent random vectors such that Xn1, ..., Xn[n[theta]] have distribution function F, and Xn[n[theta]]+1, ..., Xnn have distribution function G with F [not equal to] G. In this paper we propose an estimator [theta]n of the changepoint [theta] and show that...

In this paper we derive a general invariance principle for empirical processes indexed by smooth functions. The method is applied to prove bounds for the convergence of the empirical distributions which might be useful to verify asymptotic normality of smooth statistical functionals. As one...