On functional central limit theorems for dependent, heterogeneous arrays with applications to tail index and tail dependence estimation

Technical Appendix for "On Functional Central Limit Theorems for Dependent, Heterogenous Arrays with Applications to Tail Index and Tail Dependence Estimation"

Tail and Nontail Memory with Applications to Extreme Value and Robust Statistics

New notions of tail and nontail dependence are used to characterize separately extremal and nonextremal information, including tail log-exceedances and events, and tail-trimmed levels. We prove that near epoch dependence (McLeish, 1975; Gallant and White, 1988) and L0-approximability (Pötscher and Prucha, 1991) are equivalent for tail events and tail-trimmed levels, ensuring a Gaussian central ...

Invariance Principles for Dependent Processes Indexed by Besov Classes with an Application to a Hausman Test for Linearity

This paper considers functional central limit theorems for stationary absolutely regular mixing processes. Bounds for the entropy with bracketing are derived using recent results in Nickl and Pötscher (2007). More specifically, their bracketing metric entropy bounds are extended to a norm defined in Doukhan, Massart and Rio (1995, henceforth DMR) that depends both on the marginal distribution o...

Uniform limit theorems for the integrated periodogram of weakly dependent time series and their applications to Whittle's estimate

We prove uniform convergence results for the integrated periodogram of a weakly dependent time series, namely a law of large numbers and a central limit theorem. These results are applied to Whittle’s parametric estimation. Under general weak-dependence assumptions we derive uniform limit theorems and asymptotic normality of Whittle’s estimate for a large class of models. For instance the causa...

A New Moment Bound and Weak Laws for Mixingale Arrays without Memory or Heterogeneity Restrictions, with Applications to Tail Trimmed Arrays

We present a new weak law of large numbers for dependent heterogeneous triangular arrays fyn;tg with applications to tail trimming. The law follows from a new partial sum moment bound Ej Pn t=1 yn;tj p K Pn t=1 Ejyn;tj p for zero mean Lp-mixingale arrays fyn;t;=tg, p 2 [1; 2], where =t is a -…eld. We do not require uniform integrability, nor restrict mixingale dependence or heterogeneity. The w...