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Nonparametric Estimation of Tail Probabilities for the Single-Server Queue
Nonparametric Estimation Tail Probabilities Single-Server Queue
2015/7/8
We consider the estimation of tail probabilities in queues via the nonparametric estimator constructed by simple computing the observed fraction of time that the queue is out in the tail. We show that...
Parametric Estimation of Tail Probabilities for the Single-Server Queue
Parametric Estimation Tail Probabilities Single-Server Queue
2015/7/8
In this chapter, we consider the question of how long the arrival process to the single-server queue needs to be observed in order to accurately estimate the long-run fraction of time that the workloa...
Estimating Tail Probabilities in Queues via Extremal Statistics
Extreme values queues regenerative processes rare events estimation asymptotics
2015/7/8
We study the estimation of tail probabilities in a queue via a semi-parametric estimator based on the maximum value of the workload, observed over the sampled time interval. Logarithmic consistency an...
Tail Asymptotics for the Maximum of Perturbed Random Walk
Perturbed random walk Cramér–Lundberg approximation coupling heavy tails
2015/7/6
Consider a random walk S = (Sn:n≥0) that is “perturbed” by a stationary sequence (ξn:n≥0) to produce the process (Sn+ξn:n≥0). This paper is concerned with computing the distribution of the all-time ma...
Simple Le Cam optimal inference for the tail weight of multivariate Student $t$ distributions: testing procedures and estimation
local asymptotic normality locally asymptotically maximin tests one-step estimation Student t distribution tail weight
2013/6/14
The multivariate Student $t$ distribution is at the core of classical statistical inference and is also a well-known model for empirical financial data. In the present paper, we propose optimal (in th...
High-Frequency Tail Index Estimation by Nearly Tight Frames
High-Frequency Tail Index Estimation Nearly Tight Frames
2013/4/27
This work develops the asymptotic properties (weak consistency and Gaussianity), in the high-frequency limit, of approximate maximum likelihood estimators for the spectral parameters of Gaussian and i...
On tail trend detection: modeling relative risk
extreme value distribution regular variation extreme rainfall
2011/7/6
A simple and natural model is introduced for studying a trend in the tail of a probability distribution over time (or over space).
Multiplier bootstrap of tail copulas - with applications
copulas Multiplier bootstrap of tail applications
2011/3/18
In the problem of estimating the lower and upper tail copula we propose two bootstrap procedures for approximating the distribution of the corresponding empirical tail copulas. The first method ...
We review various inequalities for Mills' ratio (1 - \Phi)/\phi, where \phi and \Phi denote the standard Gaussian density and distribution function, respectively. Elementary considerations involving f...
Closed-form cdf and pdf of Tukey's h-distribution, the heavy-tail Lambert W approach, and how to bijectively "Gaussianize" heavy-tailed data
family of heavy-tailed distributions Tukey g-h distribution Lambert W
2010/10/19
Recently Goerg (2010) introduced Lambert W - F random variables (RVs), a new family of generalized skewed distributions. Here I will adapt this appealing framework to generate heavy (heavier) tailed ...
The tail empirical process for some long memory sequences
tail empirical process long memory sequences
2010/3/9
This paper describes limiting behaviour of tail empirical process associated with
long memory stochastic volatility models. We show that such process has dichoto-
mous behaviour, according to an int...
Estimates for tail probabilities of quadratic and bilinear forms in subgaussian random variables with applications to the law of the iterated logarithm
Estimates for tail probabilities quadratic and bilinear forms
2009/9/23
We prove upper estimates for the tail prebabibties: of
quadratic and bilinear forms in independent subgaussian randarn
vslriabb. These inequalities are used to get upper esthatcs in thc law
diterat...
Weighted least-squares estimators of tail indices
Weighted least-squares estimators tail indices
2009/9/22
We propose a class of weighted least-squares estimators
for the tail index of a regularly varying upper tail of a distribution.
Universal asymptotic normality of the estimators is established over
...
Tail probabilities for a risk process with subexponential jumps in a regenerative and diffusion environment
Ruin probability Cox process diffusion process exponential change of measure
2009/9/21
In this paper we fmd a nonexponential Lundberg approximation
of the ruin probability in a Cox model, in which a governing
process has a regenerative structure and claims are light-tailed or
have an...
Coamparision of tail probabilities of strictly stable/stable random vectors and their symmetrized counterparts with application
Stable emistable nequality
2009/9/21
It is shown that the tail probabilities of a strictly
(r, a)-semistable (0 < r < 1,0 < n < 2, a # 1) Banach space valued random
vector X and its symmetrized counterpart are "uniformly" comparable
i...