The truncated Stieltjes moment problem solved by using kernel density functions

Gavriliadis, P. N.; Athanassoulis, G. A.

doi:10.1016/j.cam.2012.05.015

Cited by 16 publications

(26 citation statements)

References 58 publications

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“…[32], the high flexibility of neural networks allows for the straightforward inclusion of additional constraints, such as the kinematic distributions of B → X u ν which will be measured with good accuracy at the upcoming Belle-II experiment [33]. The measurement of the M X or E shapes, for instance, will contribute useful information on the SFs and in turn reduce the SF uncertainty in the |V ub | extraction.…”

Section: Introductionmentioning

confidence: 99%

Neural network approach toB→Xuℓν

2016

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We use artificial neural networks to parameterize the shape functions in inclusive semileptonic B decays without charm. Our approach avoids the adoption of functional form models and allows for a straightforward implementation of all experimental and theoretical constraints on the shape functions. The results are used to extract |V ub | in the GGOU framework and compared with the original GGOU paper and the latest HFAG results, finding good agreement in both cases. The possible impact of future Belle-II data on the MX distribution is also discussed.

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Section: Introductionmentioning

confidence: 99%

Neural network approach toB→Xuℓν

2016

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“…Neither of these attempts performed as well as the do-validated bandwidth. It would be interesting to see whether indirect cross-validation and do-validation would also be useful to improve other variants of the kernel density estimation problem, such as the problem considered by Gavriliadis and Athanassoulis (2012), Park (2013), Eidous (2012) or Martínez-Miranda et al (2013).…”

Section: Simulation Experiments About Indirect Do-validationmentioning

confidence: 99%

Further theoretical and practical insight to the do-validated bandwidth selector

Mammen

Miranda

Nielsen

et al. 2014

Journal of the Korean Statistical Society

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This is the accepted version of the paper.This version of the publication may differ from the final published version. and that the recent do-validated method seems to provide the most practical alternative among these methods. In this paper we show step by step how classical cross-validation improves in theory, as well as in practice, from indirectness and that do-validated estimators improve in theory, but not in practice, from further indirectness. This paper therefore provides a strong support for the practical and theoretical properties of do-validated bandwidth selection. Do-validation is currently being introduced to survival analysis in a number of contexts and this paper provides evidence that this might be the immediate step forward. Permanent repository link

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“…Namely, first of all note that from (1) and (2) we have (5) where G(u) = F(−log b u) and ν = b −x . On the other hand, taking the derivative of with respect to u we obtain (6) with c = [αν] + 1 and d = α − [αν]. Hence, applying the integration by parts in the last integral of (5) and taking into account (6), where ν = b −x , we derive: Therefore, (7) where Ḡ(u) = 1 − G(u) = S(−log b u) and Ḡ(ν) = S(x).…”

Section: Proofmentioning

confidence: 99%

“…Here we suggest the modified, scaled version of the MR-Laplace transform inversion that enables us to apply it in the case of the Stieltjes moment problem as well, i.e., when T = ∞. The reader is referred to [3][4][5][6], where the questions on the momentdeterminacy of probability distributions and their approximations in the framework of inverse moment problem are investigated. See also Tagliani and Velasquez [7], where the fractional moments are used to approximate the Laplace transform inversion.…”

Section: Introductionmentioning

confidence: 99%

A note on recovering the distributions from exponential moments

Mnatsakanov

Sarkisian

2013

Applied Mathematics and Computation

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The problem of recovering a cumulative distribution function of a positive random variable via the scaled Laplace transform inversion is studied. The uniform upper bound of proposed approximation is derived. The approximation of a compound Poisson distribution as well as the estimation of a distribution function of the summands given the sample from a compound Poisson distribution are investigated. Applying the simulation study, the question of selecting the optimal scaling parameter of the proposed Laplace transform inversion is considered. The behavior of the approximants are demonstrated via plots and table.

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The truncated Stieltjes moment problem solved by using kernel density functions

Cited by 16 publications

References 58 publications

Neural network approach toB→Xuℓν

Neural network approach toB→Xuℓν

Further theoretical and practical insight to the do-validated bandwidth selector

A note on recovering the distributions from exponential moments

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