We propose a new class of estimators for Pickands dependence function which is based on the concept minimum distance estimation. An explicit integral representation $A^*(t)$, minimizes weighted $L^2$-distance between logarithm copula $C(y^{1-t},y^t)$ and functions form $A(t)\log(y)$ derived. If unknown an extreme-value copula, $A^*(t)$ coincides with function. Moreover, even if this not case, always satisfies boundary conditions The are obtained by replacing its empirical counterpart weak...

Two key ingredients to carry out inference on the copula of multivariate observations are empirical process and an appropriate resampling scheme for latter. Among existing techniques used i.i.d. observations, multiplier bootstrap R\'{e}millard Scaillet (J. Multivariate Anal. 100 (2009) 377-386) frequently appears lead procedures with best finite-sample properties. B\"{u}cher Ruppert 116 (2013) 208-229) recently proposed extension this technique strictly stationary strongly mixing by adapting...

In the past decades, weak convergence theory for stochastic processes has become a standard tool analyzing asymptotic properties of various statistics. Routinely, is considered in space bounded functions equipped with supremum metric. However, there are cases when those spaces fails to hold. Examples include empirical copula and tail dependence residual linear regression models case underlying distributions lack certain degree smoothness. To resolve issue, new metric locally introduced...

The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing reciprocal expected cluster size. Both disjoint and sliding blocks estimator index are analyzed detail. In contrast to many competitors, estimators only depend on choice one parameter sequence. We derive an asymptotic expansion, prove normality show consistency variance. Explicit calculations certain models finite-sample Monte Carlo simulation study...

Classical extreme value statistics consists of two fundamental approaches: the block maxima (BM) method and peak-over-threshold (POT) approach. It seems to be general consensus among researchers in field that POT approach makes use observations more efficiently than BM method. We shed light on this discussion from three different perspectives. First, based recent theoretical results for method, we provide a comparison i.i.d. scenarios. argue data generating process may favour either one or...

The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak convergence can be used to develop theory for estimators dependence measures densities, they allow derive tests stochastic independence specific structures, may serve as fundamental tool multivariate rank statistics. In present paper, we establish (for observations that allowed serially dependent)...

The block maxima method in extreme-value analysis proceeds by fitting an distribution to a sample of extracted from observed stretch time series. is usually validated under two simplifying assumptions: the should be distributed exactly according and independent. Both assumptions are only approximately true. present paper validates that can fact safely made. For general triangular arrays attracted Fréchet distribution, consistency asymptotic normality established for maximum likelihood...

We derive tests of stationarity for univariate time series by combining change‐point sensitive to changes in the contemporary distribution with serial dependence. The proposed approach relies on a general procedure dependent based resampling. After proving asymptotic validity under conjunction null hypotheses and investigating its consistency, we study rank‐based cumulative sum empirical function autocopula at given lag. Extensions solely focusing second‐order characteristics are next....

In this paper nonparametric methods to assess the multivariate Lévy measure are introduced. Starting from high-frequency observations of a process $\mathbf{X} $, we construct estimators for its tail integrals and Pareto–Lévy copula prove weak convergence these in certain function spaces. Given $n$ increments over intervals length $\Delta_{n}$, rate is $k_{n}^{-1/2}$ $k_{n}=n\Delta_{n}$ which natural concerning inference on measure. Besides extensions nonequidistant sampling schemes analytic...

For the problem of estimating lower tail and upper copulas, we propose two bootstrap procedures for approximating distribution corresponding empirical copulas. The first method uses a multiplier copula process requires estimation partial derivatives copula. second avoids this multipliers in two-dimensional function estimates marginal distributions. both procedures, prove consistency. these investigations, demonstrate that common assumption existence continuous literature on is so...

The block maxima method in extreme value theory consists of fitting an distribution to a sample extracted from time series. Traditionally, the are taken over disjoint blocks observations. Alternatively, can be chosen slide through observation period, yielding larger number overlapping blocks. Inference based on sliding is found more efficient than inference asymptotic variance maximum likelihood estimator Fréchet shape parameter reduced by 18%. Interestingly, amount efficiency gain same...

Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most corresponding theory is derived under simplifying assumption that block are independent observations from genuine distribution. In practice, however, sizes finite and different blocks dependent. Theory respecting latter complications not well developed, and, multivariate case, has only recently been established for disjoint single size. We show using overlapping instead...