Asymptotic normality of randomly truncated stochastic algorithms

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...

Almost sure convergence of randomly truncated stochastic algorithms under verifiable conditions

Abstract. In this paper, we are interested in the almost sure convergence of randomly truncated stochastic algorithms. In their pioneer work, Chen and Zhu (1986) required that the family of the noise terms is summable to ensure the convergence. In our paper, we present a new convergence theorem which extends the already known results by making vanish this condition on the noise terms — a condit...

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...

Asymptotic normality of recursive algorithms via martingale difference arrays

are such that if input data of size N produce random costs LN , then LN D = Ln + L̄N−n + RN for N ≥ n0 ≥ 2, where n follows a certain distribution PN on the integers {0, . . . ,N} and Lk D = L̄k for k ≥ 0. Ln, LN−n and RN are independent, conditional on n, and RN are random variables, which may also depend on n, corresponding to the cost of splitting the input data of size N (into subsets of size...