Nonparametric Construction of Multivariate Kernels

Panaretos, Victor M.; Konis, Kjell

doi:10.1080/01621459.2012.695657

Cited by 9 publications

(5 citation statements)

References 23 publications

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“…To implement the method requires that we choose a bandwidth h for the kernel density estimator. There has been recent work on bandwidth selection for multivariate density estimators such as Chacón andDuong (2010, 2012) and Panaretos and Konis (2012). For the purposes of this paper, we simply use the Silverman rule [Scott (1992)].…”

Section: Implementation and Examplesmentioning

confidence: 99%

Nonparametric ridge estimation

Genovese¹,

Perone-Pacifico²,

Verdinelli³

et al. 2014

Ann. Statist.

108

157

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We study the problem of estimating the ridges of a density function. Ridge estimation is an extension of mode finding and is useful for understanding the structure of a density. It can also be used to find hidden structure in point cloud data. We show that, under mild regularity conditions, the ridges of the kernel density estimator consistently estimate the ridges of the true density. When the data are noisy measurements of a manifold, we show that the ridges are close and topologically similar to the hidden manifold. To find the estimated ridges in practice, we adapt the modified mean-shift algorithm proposed by Ozertem and Erdogmus [J. Mach. Learn. Res. 12 (2011) 1249-1286]. Some numerical experiments verify that the algorithm is accurate.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1218 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Section: Implementation and Examplesmentioning

confidence: 99%

Nonparametric ridge estimation

Genovese¹,

Perone-Pacifico²,

Verdinelli³

et al. 2014

Ann. Statist.

108

157

View full text Add to dashboard Cite

show abstract

“…On the other hand, constructing a dependent model is more problematic, particulary from a nonparametric perspective. See, for example, Panaretos and Konis [2012], Wand [1992], Wand and Jones [1993], Staniswalis et al [1993], and Chacon and Duong [2018].…”

Section: Introductionmentioning

confidence: 99%

Statistical Analysis from the Fourier Integral Theorem

Ho,

Walker

2021

Preprint

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Taking the Fourier integral theorem as our starting point, in this paper we focus on natural Monte Carlo and fully nonparametric estimators of multivariate distributions and conditional distribution functions. We do this without the need for any estimated covariance matrix or dependence structure between variables. These aspects arise immediately from the integral theorem. Being able to model multivariate data sets using conditional distribution functions we can study a number of problems, such as prediction for Markov processes, estimation of mixing distribution functions which depend on covariates, and general multivariate data. Estimators are explicit Monte Carlo based and require no recursive or iterative algorithms.

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“…It would be also interesting to consider the work of Zhang et al (2013) to develop distribution free prediction sets, see Lei et al (2013). Finally, the approach of projecting a multivariate density smoother down on the structure of interest is not restricted to local linear density smoothers and could be generalised to other multivariate density smoothers including Panaretosa and Konis (2012), Xiao et al (2013) and Lu et al (2013).…”

Section: Introductionmentioning

confidence: 99%

In-sample forecasting applied to reserving and mesothelioma mortality

Mammen

Miranda

Nielsen

2015

Insurance: Mathematics and Economics

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This paper shows that recent published mortality projections with unobserved exposure can be understood as structured density estimation. The structured density is only observed on a sub-sample corresponding to historical calendar time. The mortality forecast is obtained by extrapolating the structured density to future calendar times using that the components of the density are identified within sample. The new method is illustrated on the important practical problem of forecasting mesothelioma for the UK population. Full asymptotic theory is provided. The theory is given in such generality that it also introduces mathematical statistical theory for the recent continuous chain ladder model. This allows a modern approach to classical reserving techniques used every day in any non-life insurance company around the globe. Applications to mortality data and non-life insurance data are provided along with relevant small sample simulation studies.

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Nonparametric Construction of Multivariate Kernels

Cited by 9 publications

References 23 publications

Nonparametric ridge estimation

Nonparametric ridge estimation

Statistical Analysis from the Fourier Integral Theorem

In-sample forecasting applied to reserving and mesothelioma mortality

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