Related papers: How long should a block be?
We investigate the joint asymptotic behavior of so-called blocks estimator of the extremal index, that determines the mean length of clusters of extremes, based on the exceedances over different thresholds. Due to the large bias of these…
In this paper we consider the estimation problem for high quantiles of a heavy-tailed distribution from block data when only a few largest values are observed within blocks. We propose estimators for high quantiles and prove that these…
Extreme value theory for chaotic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by…
We investigate the accuracy of two general non-parametric methods for estimating optimal block lengths for block bootstraps with time series - the first proposed in the seminal paper of Hall, Horowitz and Jing (Biometrika 82 (1995) 561-574)…
Optimal block designs in small blocks are explored when the treatments have a natural ordering and interest lies in comparing consecutive pairs of treatments. We first develop an approximate theory which leads to a convenient multiplicative…
In extreme value statistics for stationary sequences, blocks estimators are usually constructed by using disjoint blocks because exceedances over high thresholds of different blocks can be assumed asymptotically independent. In this paper…
The block maxima method is a standard approach for analyzing the extremal behavior of a potentially multivariate time series. It has recently been found that the classical approach based on disjoint block maxima may be universally improved…
We establish a general formula for the maximum size of finite length block codes with minimum pairwise distance no less than $d$. The achievability argument involves an iterative construction of a set of radius-$d$ balls, each centered at a…
Profile likelihood intervals of large quantiles in Extreme Value distributions provide a good way to estimate these parameters of interest since they take into account the asymmetry of the likelihood surface in the case of small and…
One of the most common anticipated difficulties in applying mainstream maximum likelihood inference upon extreme values is articulated on the scarcity of extreme observations for bringing the extreme value theorem to hold across a series of…
This paper investigates the use of extreme value theory for modelling the distribution of demand-net-of-wind for capacity adequacy assessment. Extreme value theory approaches are well-established and mathematically justified methods for…
In this paper, we investigate the randomized algorithms for block matrix multiplication from random sampling perspective. Based on the A-optimal design criterion, the optimal sampling probabilities and sampling block sizes are obtained. To…
The block maxima method is a classical and widely applied statistical method for time series extremes. It has recently been found that respective estimators whose asymptotics are driven by empirical means can be improved by using sliding…
Software for computation of maximum likelihood estimates in linear structural equation models typically employs general techniques from non-linear optimization, such as quasi-Newton methods. In practice, careful tuning of initial values is…
Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…
In extreme value theory, there are two fundamental approaches, both widely used: the block maxima (BM) method and the peaks-over-threshold (POT) method. Whereas much theoretical research has gone into the POT method, the BM method has not…
Ultra-Reliable Low-Latency Communications have stringent delay constraints, and hence use codes with small block length (short codewords). In these cases, classical models that provide good approximations to systems with infinitely long…
The stochastic block model (SBM) provides a popular framework for modeling community structures in networks. However, more attention has been devoted to problems concerning estimating the latent node labels and the model parameters than the…
Modelling block maxima using the generalised extreme value (GEV) distribution is a classical and widely used method for studying univariate extremes. It allows for theoretically motivated estimation of return levels, including extrapolation…
The block maxima method is one of the most popular approaches for extreme value analysis with independent and identically distributed observations in the domain of attraction of an extreme value distribution. The lack of a rigorous study on…