Asymmetric Multivariate Laplace Distribution

We consider the general problem of estimating probabilities which arise as a union of dependent events. We propose a flexible series of estimators for such probabilities, and describe variance reduction schemes applied to the proposed estimators. We derive efficiency results of the estimators in rare-event settings, in particular those associated with extremes. Finally, we examine the performance of our estimators in a numerical example.

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“…The distribution has been applied in a financial context [22], and is examined in [16,25]. From the former we have that the density of L is…”

Section: Case 2: Multivariate Laplace Distributionsmentioning

confidence: 99%

Efficient Simulation for Dependent Rare Events with Applications to Extremes

Andersen

Laub

Rojas-Nandayapa

2017

Methodol Comput Appl Probab

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“…In the simulation we choose the random vector X 1 X d to have one of the following multivariate distributions where ∈ d and the matrix = ij = is chosen as ii = 1 and ij = , with 0 < < 1, for 1 ≤ i = j ≤ d (see Liang et al, 2001, for a similar set of alternative distributions; see also Johnson, 1987;Kotz et al, 2000, for relevant information about these distributions):…”

Section: Testing Multivariate Uniformitymentioning

confidence: 99%

On the Finite Sample Behavior of Fixed Bandwidth Bickel–Rosenblatt Test for Univariate and Multivariate Uniformity

Tenreiro¹

2007

Communications in Statistics - Simulation and Computation

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The Bickel-Rosenblatt (BR) goodness-of-fit test with fixed bandwidth was introduced by Fan in 1998. Although its asymptotic properties have been studied by several authors, little is known about its finite sample performance. Restricting our attention to the test of uniformity in the d-unit cube for d ≥ 1, we present in this article a description of the finite sample behavior of the BR test as a function of the bandwidth h. For d = 1 our analysis is based not only on empirical power results but also on the Bahadur's concept of efficiency. The numerical evaluation of the Bahadur local slopes of the BR test statistic for different values of h for a set of Legendre and trigonometric alternatives give us some additional insight about the role played by the smoothing parameter in the detection of departures from the null hypothesis. For d > 1 we develop a Monte-Carlo study based on a set of meta-type uniforme alternative distributions and a rule-of-thumb for the practical choice of the bandwidth is proposed. For both univariate and multivariate cases, comparisons with existing uniformity tests are presented. The BR test reveals an overall good comparative performance, being clearly superior to the considered competiting tests for bivariate data.

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“…A multivariate extension of the GLD is obtained by using the following density generator function Kotz et al (2000):…”

Section: Elliptically Symmetric Distributions and Gaussian Scale Mixtmentioning

confidence: 99%