Local asymptotic normality of truncated empirical processes

Asymptotic normality of randomly truncated stochastic algorithms

Asymptotic normality of Hill Estimator for truncated data

The problem of estimating the tail index from truncated data is addressed in ?. In that paper, a sample based (and hence random) choice of k is suggested, and it is shown that the choice leads to a consistent estimator of the inverse of the tail index. In this paper, the second order behavior of the Hill estimator with that choice of k is studied, under some additional assumptions. In the untru...

Local Asymptotic Normality in δ-Neighborhoods of Standard Generalized Pareto Processes

De Haan and Pereira [1] provided models for spatial extremes in the case of stationarity, which depend on just one parameter β > 0 measuring tail dependence, and they proposed different estimators for this parameter. This framework was supplemented in [2] by establishing local asymptotic normality (LAN) of a corresponding point process of exceedances above a high multivariate threshold, yieldin...

asymptotic normality of the truncation probability estimator for truncated dependent data

in some long term studies, a series of dependent and possibly truncated life-times may be observed. suppose that the lifetimes have a common marginal distribution function. in left-truncation model, one observes data (xi,ti) only, when ti ≤ xi. under some regularity conditions, we provide a strong representation of the ßn estimator of ß = p(ti ≤ xi), in the form of an average of random variable...

Local Asymptotic Mixed Normality property for discretely observed stochastic differential equations driven by stable Lévy processes

We prove the Local Asymptotic Mixed Normality property from high frequency observations, of a continuous time process solution of a stochastic differential equation driven by a pure jump Lévy process. The process is observed on the fixed time interval [0, 1] and the parameter appears in the drift coefficient only. We compute the asymptotic Fisher information and find that the rate in the LAMN p...