Error bounds for kernel density estimator of spectral distribution for Gaussian Unitary Ensembles

The most important parameter in the kernel density estimator is the bandwidth or spread or window width. The bandwidth of the kernel density estimator, which follows the power law, is determined using the nearest neighborhood technique for the earthquake catalog which is divided into bins. For reliable hazard estimates, the magnitude bins used in developing the power law and estimating the spatial activity rate density function should be the same. It is important that consistency be maintained between the earthquake epicenters used in determining the bandwidth and the epicenters to which the bandwidth is applied subsequently. In this paper, the effect of epicenter data inconsistency on hazard estimates for various return periods for Chennai is evaluated. Two methods of binning are used, one in which the epicenters used in deriving the bandwidth is in line with the epicenters used in arriving at the spatial activity rate and the other where the epicenters used in deriving the bandwidth are just grouped by dividing the catalogue into equal bins. Seismic hazard estimations are compared using these two approaches of forming the magnitude bins for Chennai, Tamil Nadu, India. The peak ground acceleration (PGA) values obtained from Binning Methods 1 and 2 for 475 years return period are 0.0955g and 0.0802g respectively. The difference in PGA and peak spectral acceleration (PSA) from the two binning methods ranges from 20 to 10% with respect to Binning Method 1 for the return periods of 72 to 2475 years.

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Asymptotics for the Transformation Kernel Density Estimator

The Annals of Statistics ◽

10.1214/aos/1176324705 ◽

1995 ◽

Vol 23 (4) ◽

pp. 1198-1222 ◽

Cited By ~ 13

Author(s):

Ola Hossjer ◽

David Ruppert

Keyword(s):

Kernel Density ◽

Kernel Density Estimator ◽

Density Estimator

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New multivariate kernel density estimator for uncertain data classification

Annals of Operations Research ◽

10.1007/s10479-020-03715-4 ◽

2020 ◽

Author(s):

Byunghoon Kim ◽

Young-Seon Jeong ◽

Myong K. Jeong

Keyword(s):

Uncertain Data ◽

Kernel Density ◽

Data Classification ◽

Kernel Density Estimator ◽

Density Estimator

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An evaluation of different measures of dynamically recrystallized grain size for paleopiezometry or paleowattometry studies

Solid Earth ◽

10.5194/se-6-475-2015 ◽

2015 ◽

Vol 6 (2) ◽

pp. 475-495 ◽

Cited By ~ 20

Author(s):

M. A. Lopez-Sanchez ◽

S. Llana-Fúnez

Keyword(s):

Grain Size ◽

Kernel Density ◽

Kernel Density Estimator ◽

Gaussian Kernel ◽

Robust Estimator ◽

Density Estimator ◽

Lithospheric Deformation ◽

Single Measure ◽

Frequency Peak ◽

Recrystallized Grain Size

Abstract. Paleopiezometry and paleowattometry studies are essential to validate models of lithospheric deformation and therefore increasingly common in structural geology. These studies require a single measure of dynamically recrystallized grain size in natural mylonites to estimate the magnitude of differential paleostress (or the rate of mechanical work). This contribution tests the various measures of grain size used in the literature and proposes the frequency peak of a grain size distribution as the most robust estimator for paleopiezometry or paleowattometry studies. The novelty of the approach resides in the use of the Gaussian kernel density estimator as an alternative to the classical histograms, which improves reproducibility. A free, open-source, easy-to-handle script named GrainSizeTools ( http://www.TEOS-10.org) was developed with the aim of facilitating the adoption of this measure of grain size in paleopiezometry or paleowattometry studies. The major advantage of the script over other programs is that by using the Gaussian kernel density estimator and by avoiding manual steps in the estimation of the frequency peak, the reproducibility of results is improved.

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