Are extreme value estimation methods useful for network data?

Wan, Phyllis; Wang, Tiandong; Davis, Richard A.; Resnick, Sidney I.

doi:10.1007/s10687-019-00359-x

Cited by 26 publications

(39 citation statements)

References 24 publications

(41 reference statements)

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“…Theoretically, the linear PA network models generate power-law degree distributions, and the consistency of Hill estimators based on the non-iid degree sequences in linear PA models has been justified in [44,45]. Limit theory for degree counts in a linear PA model can be found in [4,27,26,34,35,36,42,43,44,45], and statistical inferences on the linear PA models are given in [15,40,41].…”

Section: Introductionmentioning

confidence: 99%

On a Minimum Distance Procedure for Threshold Selection in Tail Analysis

Drees¹,

Janßen²,

Resnick³

et al. 2020

SIAM Journal on Mathematics of Data Science

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Power-law distributions have been widely observed in different areas of scientific research. Practical estimation issues include how to select a threshold above which observations follow a power-law distribution and then how to estimate the power-law tail index. A minimum distance selection procedure (MDSP) is proposed in [8] and has been widely adopted in practice, especially in the analyses of social networks. However, theoretical justifications for this selection procedure remain scant. In this paper, we study the asymptotic behavior of the selected threshold and the corresponding power-law index given by the MDSP. We find that the MDSP tends to choose too high a threshold level and leads to Hill estimates with large variances and root mean squared errors for simulated data with Pareto-like tails.

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Section: Introductionmentioning

confidence: 99%

On a Minimum Distance Procedure for Threshold Selection in Tail Analysis

Drees¹,

Janßen²,

Resnick³

et al. 2020

SIAM Journal on Mathematics of Data Science

Self Cite

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“…Wan et al (2017a) also describes an approximation to the MLE that can be utilized when only a snapshot view of the network is available. Wan et al (2017b) uses a semiparametric approach to fit to the upper tail of the network degree distribution. The focus is on how the estimator performs under deviations from the linear PA model and the "superstar" linear PA model, in which one node to which most of the other nodes attach.…”

Section: Forward Model For the Imfmentioning

confidence: 99%

A preferential attachment model for the stellar initial mass function

Cisewski-Kehe

Weller²,

Schafer

2019

Electron. J. Statist.

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Accurate specification of a likelihood function is becoming increasingly difficult in many inference problems in astronomy. As sample sizes resulting from astronomical surveys continue to grow, deficiencies in the likelihood function lead to larger biases in key parameter estimates. These deficiencies result from the oversimplification of the physical processes that generated the data, and from the failure to account for observational limitations. Unfortunately, realistic models often do not yield an analytical form for the likelihood. The estimation of a stellar initial mass function (IMF) is an important example. The stellar IMF is the mass distribution of stars initially formed in a given cluster of stars, a population which is not directly observable due to stellar evolution and other disruptions and observational limitations of the cluster. There are several difficulties with specifying a likelihood in this setting since the physical processes and observational challenges result in measurable masses that cannot legitimately be considered independent draws from an IMF. This work improves inference of the IMF by using an approximate Bayesian computation approach that both accounts for observational and astrophysical effects and incorporates a physically-motivated model for star cluster formation. The methodology is illustrated via a simulation study, demonstrating that the proposed approach can recover the true posterior in realistic situations, and applied to observations from astrophysical simulation data.

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“…Nevertheless, extremal characteristics of such systems always attracted significant attention of researchers in computer science, statistical physics, financial mathematics and network studies. For example, in a recent work [43], the authors study tail indices of in-degree and out-degree of the nodes of social networks. However, they lack to justify that their methods such as Hill estimator can be extended to non-i.i.d.…”

Section: Introductionmentioning

confidence: 99%

Extremal independence in discrete random systems

Isaev¹,

Rodionov²,

Zhang³

et al. 2021

Preprint

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Let n ∈ N and X(n) = (X 1 (n), . . . , X d(n) (n)) be a sequence of random vectors. We prove that, under certain dependence conditions, the cdf of the maximum of X i (n) asymptotically equals to the cdf of the maximum of a random vector with the same but independent marginal distributions. To prove our result on extremal independence, we obtain new lower and upper bounds on the probability that none of a given finite set of events occurs. Using our result, we show that, under certain conditions, including Berman-type condition, a sequence of Gaussian random vectors possesses the extremal independence property. We also prove that certain extremal characterstics of binomial random graphs and hypergraphs, after an appropriate rescaling, have asymptotical Gumbel distribution (in particular, maximum codegrees in random hypergraphs and the maximum number of cliques sharing a given vertex in random graphs).

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Are extreme value estimation methods useful for network data?

Cited by 26 publications

References 24 publications

On a Minimum Distance Procedure for Threshold Selection in Tail Analysis

On a Minimum Distance Procedure for Threshold Selection in Tail Analysis

A preferential attachment model for the stellar initial mass function

Extremal independence in discrete random systems

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