Test for the existence of finite moments via bootstrap

Ng, Wai Leong; Yau, Chun Yip

doi:10.1080/10485252.2017.1402896

Cited by 4 publications

(5 citation statements)

References 37 publications

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“…In order to further confirm this result, we perform the bootstrap test (see [22]). We test the existence of the p-th moment for p ∈ {1, 2, 3, 4, 5, 6, 7, 8} using M = 10 7 samples of the subordinated evaluated GRF L(1, 1).…”

Section: Statistical Methods To Test the Existence Of Moments Of A Ra...mentioning

confidence: 89%

“…Nevertheless, in the literature only few statistical methods exist to verify or disprove the existence of moments, given a specific sample of random variables (see e.g. [20,15,22,10,12,11]) . One of the earlier methods to verify the existence of moments of a distribution was proposed in 1963 by Mandelbrot (see [20] and [8]).…”

Section: Statistical Methods To Test the Existence Of Moments Of A Ra...mentioning

confidence: 99%

“…Another popular direct way to investigate the existence of moments of a certain distribution is the sample-based estimation of a decay rate α for the corresponding density function proposed by Hill in [15]. However, the Hill-estimator requires a parameter k > 0 which specifies the sample values which are considered as the tail of the distribution and it turned out that the Hill-estimator is very sensitive to the choice of this parameter k. Further, the method makes the quite restrictive assumption that the underlying distribution is of Pareto-type (see [22,10,12] and [11]). In 2013, Fedotenkov proposed a bootstrap test for the existence of moments of a given distribution (see [10]).…”

Section: Statistical Methods To Test the Existence Of Moments Of A Ra...mentioning

confidence: 99%

“…The test performs well for specific distributions, however, its accuracy deteriorates fast when moments of higher order are considered (see also [12]). Recently, Ng and Yau proposed another sample-based bootstrap test for the existence of moments which outperforms the previously mentioned methods for many distributions (see [22]). The test is based on a result from bootstrap asymptotic theory which states that the m out of n bootstrap sample mean (see [7]) converges weakly to a normal distribution.…”

Section: Statistical Methods To Test the Existence Of Moments Of A Ra...mentioning

confidence: 99%

“…The test is based on a result from bootstrap asymptotic theory which states that the m out of n bootstrap sample mean (see [7]) converges weakly to a normal distribution. For details we refer to [22].…”

Section: Statistical Methods To Test the Existence Of Moments Of A Ra...mentioning

confidence: 99%

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Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal distribution of the constructed random fields, derive a Lévy-Khinchin-type formula and semiexplicit formulas for the covariance function. Further, we study the pointwise stochastic regularity and validate our theoretical findings in various numerical examples.

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Section: Statistical Methods To Test the Existence Of Moments Of A Ra...mentioning

confidence: 89%

Section: Statistical Methods To Test the Existence Of Moments Of A Ra...mentioning

confidence: 99%

Section: Statistical Methods To Test the Existence Of Moments Of A Ra...mentioning

confidence: 99%

Section: Statistical Methods To Test the Existence Of Moments Of A Ra...mentioning

confidence: 99%

Section: Statistical Methods To Test the Existence Of Moments Of A Ra...mentioning

confidence: 99%

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Some measures of kurtosis and their inference on large datasets

Borroni

Capitani

2022

AStA Adv Stat Anal

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This paper deals with the estimation of kurtosis on large datasets. It aims at overcoming two frequent limitations in applications: first, Pearson's standardized fourth moment is computed as a unique measure of kurtosis; second, the fact that data might be just samples is neglected, so that the opportunity of using suitable inferential tools, like standard errors and confidence intervals, is discarded. In the paper, some recent indexes of kurtosis are reviewed as alternatives to Pearson’s standardized fourth moment. The asymptotic distribution of their natural estimators is derived, and it is used as a tool to evaluate efficiency and to build confidence intervals. A simulation study is also conducted to provide practical indications about the choice of a suitable index. As a conclusion, researchers are warned against the use of classical Pearson’s index when the sample size is too low and/or the distribution is skewed and/or heavy-tailed. Specifically, the occurrence of heavy tails can deprive Pearson’s index of any meaning or produce unreliable confidence intervals. However, such limitations can be overcome by reverting to the reviewed alternative indexes, relying just on low-order moments.

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On Some Distributional Properties of Subordinated Gaussian Random Fields

Merkle

Barth

2022

Methodol Comput Appl Probab

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Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal distribution of the constructed random fields, derive a Lévy-Khinchin-type formula and semi-explicit formulas for the covariance function. Further, we study the pointwise stochastic regularity and present various numerical examples.

show abstract

Test for the existence of finite moments via bootstrap

Cited by 4 publications

References 37 publications

Subordinated Gaussian Random Fields

Subordinated Gaussian Random Fields

Some measures of kurtosis and their inference on large datasets

On Some Distributional Properties of Subordinated Gaussian Random Fields

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