Re-formulation of inverse Gaussian, reciprocal inverse Gaussian, and Birnbaum–Saunders kernel estimators

Igarashi, Gaku; Kakizawa, Yoshihide

doi:10.1016/j.spl.2013.10.013

Cited by 40 publications

(27 citation statements)

References 13 publications

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“…Although more types of asymmetric kernels, such as log-normal and Birnbaum-Saunders (Jin and Kawczak, 2003) or Inverse Gaussian and reciprocal Inverse Gaussian (Scaillet, 2004), were investigated in the subsequent literature, those showed little advantage over Chen's Gamma kernel density estimator which arguably remains the main reference for asymmetric kernel estimation on R + . Its properties were further investigated in Bouezmarni and Scaillet (2005), Hagmann and Scaillet (2007), Zhang (2010) and Malec and Schienle (2014), and other ideas related to asymmetric kernel estimation were described in Kuruwita et al (2010), Comte and Genon-Catalot (2012), Mnatsakanov and Sarkisian (2012), Jeon and Kim (2013), Koul and Song (2013), Marchant et al (2013), Igarashi and Kakizawa (2014) and Igarashi (2016). Recently, Hirukawa and Sakudo (2015) described a family of 'generalised Gamma kernels' which includes a variety of similar asymmetric kernels in an attempt to standardise those results.…”

Section: Introductionmentioning

confidence: 99%

Local-Likelihood Transformation Kernel Density Estimation for Positive Random Variables

Geenens

Wang

2018

Journal of Computational and Graphical Statistics

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The kernel estimator is known not to be adequate for estimating the density of a positive random variable X. The main reason is the well-known boundary bias problems that it suffers from, but also its poor behaviour in the long right tail that such a density typically exhibits. A natural approach to this problem is to first estimate the density of the logarithm of X, and obtaining an estimate of the density of X using standard results on functions of random variables ('back-transformation'). Although intuitive, the basic application of this idea yields very poor results, as was documented earlier in the literature. In this paper, the main reason for this underachievement is identified, and an easy fix is suggested. It is demonstrated that combining the transformation with local likelihood density estimation methods produces very good estimators of R + -supported densities, not only close to the boundary, but also in the right tail. The asymptotic properties of the proposed 'local likelihood transformation kernel density estimators' are derived for a generic transformation, not only for the logarithm, which allows one to consider other transformations as well. One of them, called the 'probex' transformation, is given more focus. Finally, the excellent behaviour of those estimators in practice is evidenced through a comprehensive simulation study and the analysis of several real data sets. A nice consequence of articulating the method around local-likelihood estimation is that the resulting density estimates are typically smooth and visually pleasant, without oversmoothing important features of the underlying density.

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Section: Introductionmentioning

confidence: 99%

Local-Likelihood Transformation Kernel Density Estimation for Positive Random Variables

Geenens

Wang

2018

Journal of Computational and Graphical Statistics

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“…The ratios of modified Bessel functions I ν (x)/I ν−1 (x) and K ν (x)/K ν−1 (x) are important quantities appearing in a large number of scientific applications. Bounds for these ratios have been recently used in connection with Schwarz methods for reaction-diffusion processes [3], statistics [7,11] and in the study of oscillatory solutions of second order ODEs [5]. See [12] and references cited therein for additional examples of application of these bounds; see also [4,1,9,8,6,2] for additional papers exploring different methods for bounding these ratios.…”

Section: Introductionmentioning

confidence: 99%

A new type of sharp bounds for ratios of modified Bessel functions

Ruiz-Antolín

Segura

2016

Journal of Mathematical Analysis and Applications

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The bounds for the ratios of first and second kind modified Bessel functions of consecutive orders are important quantities appearing in a large number of scientific applications. We obtain new bounds which are accurate in a large region of parameters and which are shaper than previous bounds. The new bounds are obtained by a qualitative analysis of the Riccati equation satisfied by these ratios. A procedure is considered in which the bounds obtained from the analysis of the Riccati equation are used to define a new function satisfying a new Riccati equation which yields sharper bounds. Similar ideas can be applied to other functions.

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“…Mnatsakanov and Sarkisian (2012), Koul and Song (2013), Marchant et al (2013), and Saulo et al (2013) studied other asymmetric kernel estimators. Igarashi and Kakizawa (2014) indicated the boundary problem of the BS, IG, and RIG kernel estimators, and re-formulated these estimators to avoid the problem. Also, Igarashi (2016) pointed out the boundary problem of the LN kernel estimator and suggested a weighted LN kernel estimator that does not have the boundary problem.…”

Section: Suggested Inversementioning

confidence: 99%

Multivariate Density Estimation Using a Multivariate Weighted Log-Normal Kernel

Igarashi

2018

Sankhya A

Self Cite

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This paper suggests a multivariate asymmetric kernel density estimator using a multivariate weighted log-normal (LN) kernel for non-negative multivariate data. Asymptotic properties of the multivariate weighted LN kernel estimator are studied. Simulation studies are also conducted to investigate the finite sample performance of the multivariate weighted LN kernel estimator in the bivariate situation.

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Re-formulation of inverse Gaussian, reciprocal inverse Gaussian, and Birnbaum–Saunders kernel estimators

Cited by 40 publications

References 13 publications

Local-Likelihood Transformation Kernel Density Estimation for Positive Random Variables

Local-Likelihood Transformation Kernel Density Estimation for Positive Random Variables

A new type of sharp bounds for ratios of modified Bessel functions

Multivariate Density Estimation Using a Multivariate Weighted Log-Normal Kernel

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