Ke-Ang Fu

Some Limit Theorems for Linear Processes Generated by Symmetrically Exchangeable Random Variables

For the linear process , where {a i ; i ≥ 0} is an absolutely summable sequence of real numbers, and {ϵ i ; − ∞ <i < ∞} is a doubly infinite sequence of symmetrically exchangeable random variables with zero means and finite variances, some limit theorems, including the central limit theorem, complete convergence and the law of iterated logarithm, are obtained for the partial sums of the linear processes.

Strong laws of large numbers for arrays of rowwise independent random compact sets and fuzzy random sets

In this paper we obtain some strong laws of large numbers (SLLNs) for arrays of rowwise independent (not necessary identically distributed) random compact sets and fuzzy random sets whose underlying spaces are separable Banach spaces.

Strong limit theorems for random sets and fuzzy random sets with slowly varying weights

Theories of random sets and fuzzy random sets are useful concepts which are frequently applied in scientific areas including information science, probability and statistics. In this paper strong limit theorems are derived for random sets and fuzzy random sets with slowly varying weights in separable Banach spaces. Both independent and dependent cases are covered to provide a wide range of applications.

Moderate deviations for sums of dependent claims in a size-dependent renewal risk model

ABSTRACT In this article, we consider a non standard renewal risk model, in which pairs of claim sizes and its corresponding inter-arrival times are identically distributed, and each pair obeys a dependence structure. By assuming that the claim sizes form a sequence of extended negatively dependent random variables with consistently varying tails, moderate deviations for the aggregate amount of dependent claims are obtained.

Asymptotic Properties of the R/S Statistics for Linear Processes

Let {X k ; k ≥ 1} be a linear process defined by where {ϵ i ; − ∞ <i < ∞} is a doubly infinite sequence of i.i.d. random variables, and . Denote the R/S statistic by Q(n) = R(n)/S(n), where , and are the adjust range of partial sums, the sample mean, and the sample variance, respectively. In this article, the exact moment convergence rates in the law of the iterated logarithm, the law of the logarithm and the complete convergence for R/S statistics are achieved, when may be infinite.

Precise asymptotics for the first moment of the error variance estimator in linear models

Abstract Let σ 2 be the unknown error variance of a linear model and let σ ˆ 2 be the estimator of σ 2 based on the residual sum of squares. In this work, we show the precise asymptotics in the law of the logarithm for the first moment of the error variance estimator.

An Application of U-Statistics to Nonparametric Functional Data Analysis

Functional regression functions, with explanatory variables taking values in some abstract function space, have been studied extensively. In this article, we aim to investigate the multivariate functional regression function, and propose a nonparametric estimator for the multivariate case. By applying some properties of U-statistics, some asymptotic distributions of such estimator are obtained under different cases.

Exact Moment Convergence Rates of U-Statistics

Let U n be a U-statistic based on a symmetric kernel h(x, y) and i.i.d. samples {X, X n ; n ≥ 1}. In this article, the exact moment convergence rates in the first moment of U n are obtained, which extend previous results concerning partial sums.

Precise large deviations of aggregate claims in a risk model with size dependence and non stationary arrivals

ABSTRACT Consider a risk model with claims of heavy tails for non stationary arrival processes that satisfy a large-deviation principle. Assume that the claim sizes and interarrival times form a sequence of random pairs, with each pair obeying a dependence structure via the conditional distribution of the interarrival time given the subsequent claim size being large, and then a precise large-deviation formula of the aggregate amount of claims is obtained.

Tail behavior for the sum of two correlated classes of discounted aggregate claims in a time-dependent risk model

ABSTRACT Consider a continuous-time risk model with two correlated classes of insurance business and a constant force of interest. Suppose that the correlation comes from a common shock, and that the claim sizes and inter-arrival times correspondingly form a sequence of random pairs, with each pair obeying a dependence structure. By assuming that the claim sizes are heavy tailed, a uniform tail asymptotic formula for the sum of the two correlated classes of discounted aggregate claims is obtained.