Bias corrections for some asymmetric kernel estimators

Igarashi, Gaku; Kakizawa, Yoshihide

doi:10.1016/j.jspi.2014.11.003

Cited by 25 publications

(18 citation statements)

References 17 publications

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“…(see Igarashi and Kakizawa (2015)), which yield the exponential convergence of the two-sided tail probability of f…”

Section: Remarkmentioning

confidence: 94%

“…Note that the additive estimator (3) is a linear combination of g β (x) and (∂/∂β) g β (x), as in a generalized jackknifing estimator (Jones and Foster (1993;Example 2.3)) for the standard kernel density estimator (S = R). See also Igarashi and Kakizawa (2015) for the gamma/MIG/weighted LN kernel density estimators (S = [0, ∞)), and Igarashi (2016a) for the beta kernel density estimator (S = [0, 1]).…”

Section: General Methodology Of Bias Reductionmentioning

confidence: 99%

“…The present setting I q,ι 0 [r b ] is preferable to the previous setting in Igarashi and Kakizawa (2015), since the former enables us to define the speed r b → ∞ more concretely.…”

Section: Limiting Jf 1 (=Ts 1 ) Type Bias-reduced Amoroso Kernel Densmentioning

confidence: 99%

“…Surprisingly, the factor {λ 4 (a)/a} 2/9 (see Corollaries 5 and 10 (i)) is common even for other SS a /TS a type bias-reduced MIG/weighted LN/beta kernel density estimators (Igarashi and Kakizawa (2015) for the case S = [0, ∞) and Igarashi (2016a) for the case S = [0, 1]), as well as the standard kernel density estimator using the Gaussian-based fourth-order kernel for the case S = R (Wand and Schucany (1990)). It would be interesting to discuss the conditions under which the factor appears in the AMISE of the asymmetric kernel density estimation, but it is left as a topic for future work, though, as in Koul and Song (2013), the approximation to the Gaussian kernel may be related to this issue.…”

Section: Concluding Remarkmentioning

confidence: 99%

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Limiting bias-reduced Amoroso kernel density estimators for non-negative data

Igarashi

Kakizawa

2017

Communications in Statistics - Theory and Methods

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The Amoroso kernel density estimator ) for nonnegative data is boundary-bias-free and has the mean integrated squared error (MISE) of order O(n −4/5 ), where n is the sample size. In this paper, we construct a linear combination of the Amoroso kernel density estimator and its derivative with respect to the smoothing parameter. Also, we propose a related multiplicative estimator. We show that the MISEs of these bias-reduced estimators achieve the convergence rates n −8/9 , if the underlying density is four times continuously differentiable. We illustrate the finite sample performance of the proposed estimators, through the simulations.

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“…(see Igarashi and Kakizawa (2015)), which yield the exponential convergence of the two-sided tail probability of f…”

Section: Remarkmentioning

confidence: 94%

Section: General Methodology Of Bias Reductionmentioning

confidence: 99%

“…The present setting I q,ι 0 [r b ] is preferable to the previous setting in Igarashi and Kakizawa (2015), since the former enables us to define the speed r b → ∞ more concretely.…”

Section: Limiting Jf 1 (=Ts 1 ) Type Bias-reduced Amoroso Kernel Densmentioning

confidence: 99%

Section: Concluding Remarkmentioning

confidence: 99%

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Limiting bias-reduced Amoroso kernel density estimators for non-negative data

Igarashi

Kakizawa

2017

Communications in Statistics - Theory and Methods

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“…Also recently, Libengué (2013) investigated several families of these univariate continuous kernels that he called univariate associated kernels; see also Kokonendji et al (2007), Kokonendji and Senga Kiéssé (2011), Zougab et al (2012Zougab et al ( , 2013 for univariate discrete situations. This procedure cancels of course the boundary bias; however, it creates a quantity in the bias of the estimator which needs reduction; see, for instance, Malec and Schienle (2014), Hirukawa and Sakudo (2014) and Igarashi and Kakizawa (2015).…”

Section: Introductionmentioning

confidence: 99%

On multivariate associated kernels to estimate general density functions

Kokonendji

Somé²

2018

Journal of the Korean Statistical Society

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Multivariate associated kernel estimators, which depend on both target point and bandwidth matrix, are appropriate for partially or totally bounded distributions and generalize the classical ones as Gaussian. Previous studies on multivariate associated kernels have been restricted to product of univariate associated kernels, also considered having diagonal bandwidth matrices. However, it is shown in classical cases that for certain forms of target density such as multimodal, the use of full bandwidth matrices offers the potential for significantly improved density estimation. In this paper, general associated kernel estimators with correlation structure are introduced. Properties of these estimators are presented; in particular, the boundary bias is investigated. Then, the generalized bivariate beta kernels are handled with more details. The associated kernel with a correlation structure is built with a variant of the mode-dispersion method and two families of bandwidth matrices are discussed under the criterion of cross-validation. Several simulation studies are done. In the particular situation of bivariate beta kernels, it is therefore pointed out the very good performance of associated kernel estimators with correlation structure compared to the diagonal case. Finally, an illustration on real dataset of paired rates in a framework of political elections is presented.

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Light- and Heavy-Tailed Density Estimation by Gamma-Weibull Kernel

Markovich

2018

Springer Proceedings in Mathematics &Amp; Statistics

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Bias corrections for some asymmetric kernel estimators

Cited by 25 publications

References 17 publications

Limiting bias-reduced Amoroso kernel density estimators for non-negative data

Limiting bias-reduced Amoroso kernel density estimators for non-negative data

On multivariate associated kernels to estimate general density functions

Light- and Heavy-Tailed Density Estimation by Gamma-Weibull Kernel

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