Berry–Esseen theorems under weak dependence

Coupled Fixed Point Theorems under Weak Contractions

Critical fixed point theorems in Banach algebras under weak topology features

In this paper, we establish some new critical fixed point theorems for the sum $AB+C$ in a Banach algebra relative to the weak topology, where $frac{I-C}{A}$ allows to be noninvertible. In addition, a special class of Banach algebras will be considered.

Weak Lefschetz Theorems

A new approach to Nori's weak Lefschetz theorem is described. The new approach, which involves the ¯ ∂-method, avoids moving arguments and gives much stronger results. In particular, it is proved that if X and Y are connected smooth projective varieties of positive dimension and f : Y − → X is a holomorphic immersion with ample normal bundle, then the image of π 1 (Y) in π 1 (X) is of finite in...

Asymptotic Theory for Nonlinear Quantile Regression under Weak Dependence

This paper studies the asymptotic properties of the nonlinear quantile regression model under general assumptions on the error process, which is allowed to be heterogeneous and mixing. We derive the consistency and asymptotic normality of regression quantiles under mild assumptions. First-order asymptotic theory is completed by a discussion of consistent covariance estimation.

A Berry-Esseen Theorem for Sample Quantiles Under Weak Dependence

This paper proves a Berry–Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be O(n) as n→∞, where n denotes the sample size. This result is in sharp contrast to the case of the sample mean of strongly-mixing random variables where the rate O(n) is not known even under an exponential strong mixing ...