Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications

Functional limit laws for the increments of the quantile process; with applications

We establish a functional limit law of the logarithm for the increments of the normed quantile process based upon a random sample of size n → ∞. We extend a limit law obtained by Deheuvels and Mason (12), showing that their results hold uniformly over the bandwidth h, restricted to vary in [h n , h n ], where {h n } n≥1 and {h ′′ n } n≥1 are appropriate nonrandom sequences. We treat the case wh...

Non standard functional limit laws for the increments of the compound empirical distribution function

Kaplan–Meier Estimator

The Kaplan–Meier estimator is a nonparametric estimator which may be used to estimate the survival distribution function from censored data. The estimator may be obtained as the limiting case of the classical actuarial (life table) estimator, and it seems to have been first proposed by Böhmer [2]. It was, however, lost sight of by later researchers and not investigated further until the importa...

Functional limit theorems for linear processes in the domain of attraction of stable laws

We study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with infinite variance and in the domain of attraction of stable laws.

Limit Laws for Random Exponentials

We study the limiting distribution of the sum SN (t) = ∑N i=1 e tXi as t→∞, N →∞, where (Xi) are i.i.d. random variables. Attention to such exponential sums has been motivated by various problems in the theory of random media. Examples include the quenched mean population size of branching random processes with random branching rates and the partition function of Derrida’s Random Energy Model. ...