Nonparametric Analysis of Univariate Heavy‐Tailed Data

Markovich, Natalia M.

doi:10.1002/9780470723609

Cited by 81 publications

(51 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since then, similar heavy-tailed distributions have been empirically found in other financial situations [2-4, 16, 22, 23], and in many other application areas [1,8,13,15,20].…”

Section: Case Of Heavy-tailed Distribution: Second Related Problemsupporting

confidence: 56%

How to Detect Linear Dependence on the Copula Level?

Kreinovich

Nguyen

Sriboonchitta

2014

Modeling Dependence in Econometrics

View full text Add to dashboard Cite

Abstract. In many practical situations, the dependence between the quantities is linear or approximately linear. Knowing that the dependence is linear simplifies computations; so, is is desirable to detect linear dependencies. If we know the joint probability distribution, we can detect linear dependence by computing Pearson's correlation coefficient. In practice, we often have a copula instead of a full distribution; in this case, we face a problem of detecting linear dependence based on the copula. Also, distributions are often heavy-tailed, with infinite variances, in which case Pearson's formulas cannot be applied. In this paper, we show how to modify Pearson's formula so that it can be applied to copulas and to heavy-tailed distributions.

show abstract

“…Since then, similar heavy-tailed distributions have been empirically found in other financial situations [2-4, 16, 22, 23], and in many other application areas [1,8,13,15,20].…”

Section: Case Of Heavy-tailed Distribution: Second Related Problemsupporting

confidence: 56%

How to Detect Linear Dependence on the Copula Level?

Kreinovich

Nguyen

Sriboonchitta

2014

Modeling Dependence in Econometrics

View full text Add to dashboard Cite

show abstract

“…Also, we introduced inverse gamma and lognormal kernels for densities with support (0, ∞) as well as the Pareto kernel for extreme cases (e.g. Markovich (2007)). From Part (b) of Figure 1 one can observe the inside disfunctioning of inverse Gaussian and inverse gamma kernels.…”

Section: Extended Beta Kernelmentioning

confidence: 99%

The mode-dispersion approach for constructing continuous associated kernels

Dolele-Kpok¹,

Kokonendji²

2017

JAS

View full text Add to dashboard Cite

Abstract. We introduce the mode-dispersion approach for constructing the (asymmetric) continuous associated kernels from suitable parametric probability density functions (p.d.f.) that we shall call the type of kernel. This leads us to value the choice of the associated kernel, since it takes into account the support of the unknown density f , to be estimated. All associated kernel density estimators must be without edge effect. For illustrating this, we introduce the extended beta kernel, which is a typical model of kernels with bounded supports. However, in the presence of a large bias of the density estimator, we propose a general but light modification in the same type of the first associated kernel; it leads to improve the mean integrated square error of the new estimator. Some properties of two estimators are investigated and compared, in particular pointwise and global (asymptotical) properties. Several forms of types of kernels and their associated kernel estimators are subsequently examined in detail. Simulation studies are made on three lognormal kernel density estimators for pointing out some behaviors at the boundaries. 1418Résumé. Nous introduisons l'approche mode-dispersion pour la construction des noyaux associés continus (asymétrique) à partir des fonctions de densité de probabilités (f.d.p.) paramétrées que nous appelons type de noyau. Ceci nous conduit à valoriser le choix du noyau associé puisque celui-ci tient compte du support de la densité inconnue f , à estimer. Tous les estimateurs à noyaux associés de densité sont sans effet de bord. Pour illustrer ceci, nous introduisons le noyau associé bêta étendu, qui est un modèle type des noyaux à supports bornés. Cependant, en présence d'un grand biais de l'estimateur à noyaux associés de densité, nous proposons une technique de modification générale mais légère dans le même type du premier noyau associé ; Cela conduit à réduire l'erreur quadratique moyenne intégrée du nouvel estimateur. Certaines propriétés de deux estimateurs sont étudiées et comparées, en particulier des propriétés asymptotiques ponctuelles et globales. Plusieurs formes de types de noyaux et leurs estimateurs à noyaux associés sont ensuite examinés en détail. Des études de simulation sont faites sur trois estimateurs de densité à noyau log-normal pour souligner les comportements aux bords.

show abstract

“…Herein, this paper proposes to measure the PDF samples by the kernel density estimation (KDE) method, i.e., the ParzenRosenblatt window method [10,11].…”

Section: Zmnl Sample Calculation Via the Kdementioning

confidence: 99%

Locally optimal detector design in impulsive noise with unknown distribution

Luo

Peng

Zhang

2018

EURASIP J. Adv. Signal Process.

View full text Add to dashboard Cite

This paper designs the locally optimal detector (LOD) in additive white impulsive noise with unknown distribution. Unlike traditional LODs derived from a known or approximated noise probability density function (PDF), the LOD proposed in this paper is achieved by designing the zero-memory non-linearity (ZMNL) function based on real data. After the PDF estimation in a nonparametric way by a kernel method, the ZMNL function is designed as a piecewise differentiable function consisting of a polynomial function and inverse proportional functions. Then, we analyze the detection performance and develop the constant false alarm ratio technique. Simulation results show that the LOD design is near-optimal in α-stable noise and the optimal in real atmospheric data, compared with the maximum likelihood detector of α-stable distribution.

show abstract

Nonparametric Analysis of Univariate Heavy‐Tailed Data

Cited by 81 publications

References 0 publications

How to Detect Linear Dependence on the Copula Level?

How to Detect Linear Dependence on the Copula Level?

The mode-dispersion approach for constructing continuous associated kernels

Locally optimal detector design in impulsive noise with unknown distribution

Contact Info

Product

Resources

About