Related papers: Adapting the Hill estimator to distributed inferen…
We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…
Modeling and understanding multivariate extreme events is challenging, but of great importance in various applications - e.g. in biostatistics, climatology, and finance. The separating Hill estimator can be used in estimating the extreme…
A new estimator is proposed for estimating the tail exponent of a heavy-tailed distribution. This estimator, referred to as the layered Hill estimator, is a generalization of the traditional Hill estimator, building upon a layered structure…
In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not…
The Hill estimator is often used to infer the power behavior in tails of experimental distribution functions. This estimator is known to produce bad results in certain situations which have lead to the so-called Hill horror plots. In this…
The development of modern technology has enabled data collection of unprecedented size, which poses new challenges to many statistical estimation and inference problems. This paper studies the maximum score estimator of a semi-parametric…
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…
The proliferation of science and technology has led to the prevalence of voluminous data sets that are distributed across multiple machines. It is an established fact that conventional statistical methodologies may be unfeasible in the…
This paper investigates pooling strategies for tail index and extreme quantile estimation from heavy-tailed data. To fully exploit the information contained in several samples, we present general weighted pooled Hill estimators of the tail…
A wide range of natural and social phenomena result in observables whose distributions can be well approximated by a power-law decay. The well-known Hill estimator of the tail exponent provides results which are in many respects superior to…
In this paper we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree…
We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…
In multicenter research, individual-level data are often protected against sharing across sites. To overcome the barrier of data sharing, many distributed algorithms, which only require sharing aggregated information, have been developed.…
The debiased estimator is a crucial tool in statistical inference for high-dimensional model parameters. However, constructing such an estimator involves estimating the high-dimensional inverse Hessian matrix, incurring significant…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
Distributed data naturally arise in scenarios involving multiple sources of observations, each stored at a different location. Directly pooling all the data together is often prohibited due to limited bandwidth and storage, or due to…
We propose a new weighted average estimator for the high dimensional parameters under the distributed learning system, in which the weight assigned to each coordinate is precisely proportional to the inverse of the variance of the local…
This work addresses the distributed estimation problem in a set membership framework. The agents of a network collect measurements which are affected by bounded errors, thus implying that the unknown parameters to be estimated belong to a…
When analysing extreme values, two alternative statistical approaches have historically been held in contention: the block maxima method (or annual maxima method, spurred by hydrological applications) and the peaks-over-threshold. Clamoured…
This paper considers distributed M-estimation under heterogeneous distributions among distributed data blocks. A weighted distributed estimator is proposed to improve the efficiency of the standard "Split-And-Conquer" (SaC) estimator for…