Recent Developments in Nonparametric Density Estimation

Izenman, Alan Julian

doi:10.2307/2289732

Cited by 348 publications

(276 citation statements)

References 160 publications

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“…The solid black curve is the sum of the solid gray and dotted curves, and corresponds to the net distribution for which the likelihood in Equation (2) is maximized. The name and apparent B magnitude of the galaxy are indicated in the upper left corner of the left panel, where we also quote the total number of sources in each histogram and the bin width h. The width of the bins, used only for display purposes here, follows the rule h = 2(IQR)N −1/3 , where (IQR) is the interquartile range of the magnitude distribution and N is the total number of objects in each GC sample (Izenman 1991).…”

Section: Gclf Model Fittingmentioning

confidence: 99%

The Acs Fornax Cluster Survey. Viii. The Luminosity Function of Globular Clusters in Virgo and Fornax Early-Type Galaxies and Its Use as a Distance Indicator

Villegas

Jordán

Peng

et al. 2010

ApJ

169

189

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We use a highly homogeneous set of data from 132 early-type galaxies in the Virgo and Fornax clusters in order to study the properties of the globular cluster luminosity function (GCLF). The globular cluster system of each galaxy was studied using a maximum likelihood approach to model the intrinsic GCLF after accounting for contamination and completeness effects. The results presented here update our Virgo measurements and confirm our previous results showing a tight correlation between the dispersion of the GCLF and the absolute magnitude of the parent galaxy. Regarding the use of the GCLF as a standard candle, we have found that the relative distance modulus between the Virgo and Fornax clusters is systematically lower than the one derived by other distance estimators, and in particular, it is 0.22 mag lower than the value derived from surface brightness fluctuation measurements performed on the same data. From numerical simulations aimed at reproducing the observed dispersion of the value of the turnover magnitude in each galaxy cluster we estimate an intrinsic dispersion on this parameter of 0.21 mag and 0.15 mag for Virgo and Fornax, respectively. All in all, our study shows that the GCLF properties vary systematically with galaxy mass showing no evidence for a dichotomy between giant and dwarf early-type galaxies. These properties may be influenced by the cluster environment as suggested by cosmological simulations.

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Section: Gclf Model Fittingmentioning

confidence: 99%

The Acs Fornax Cluster Survey. Viii. The Luminosity Function of Globular Clusters in Virgo and Fornax Early-Type Galaxies and Its Use as a Distance Indicator

Villegas

Jordán

Peng

et al. 2010

ApJ

169

189

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“…Between two discretization points, the PDF is described by a linear function. This interval is referred to as a bin (Izenman 1991). A calculation method with discretized PDFs is described before in Jaroszewicz and Korzeń (2012) and Korzeń and Jaroszewicz (2014).…”

Section: Piecewise Linear Pdfsmentioning

confidence: 99%

Uncertainty propagation of arbitrary probability density functions applied to upscaling of transmissivities

Lourens

Geer

2015

Stoch Environ Res Risk Assess

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In many fields of study, and certainly in hydrogeology, uncertainty propagation is a recurring subject. Usually, parametrized probability density functions (PDFs) are used to represent data uncertainty, which limits their use to particular distributions. Often, this problem is solved by Monte Carlo simulation, with the disadvantage that one needs a large number of calculations to achieve reliable results. In this paper, a method is proposed based on a piecewise linear approximation of PDFs. The uncertainty propagation with these discretized PDFs is distribution independent. The method is applied to the upscaling of transmissivity data, and carried out in two steps: the vertical upscaling of conductivity values from borehole data to aquifer scale, and the spatial interpolation of the transmissivities. The results of this first step are complete PDFs of the transmissivities at borehole locations reflecting the uncertainties of the conductivities and the layer thicknesses. The second step results in a spatially distributed transmissivity field with a complete PDF at every grid cell. We argue that the proposed method is applicable to a wide range of uncertainty propagation problems.

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“…It follows from the fact that the "random EEG" relative displacement ΔY τ (obtained from m-dimensional vector X(t) whose components are independent normal random variables having zero mean and variance σ 2 ) is distributed according to the chi distribution that is a special case of (2) [6] and [7] suggestions respecttively, where IQR τ is the interquartile range defined as the 75th percentile minus the 25th percentile, and σ τ is the standard deviation of the distribution. The number of bins h τ is defined as entire(max(ΔY τ )/W τ ) + 1.…”

Section: Eeg Data Analysismentioning

confidence: 99%

Age-Related Changes in Probability Density Function of Pairwise Euclidean Distances between Multichannel Human EEG Signals

Trifonov¹,

Rozhkov²

2014

JBM

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The probability density functions (pdf's) and the first order structure functions (SF's) of the pairwise Euclidean distances between scaled multichannel human EEG signals at different time lags under hypoxia and in resting state at different ages are estimated. It is found that the hyper gamma distribution is a good fit for the empirically derived pdf in all cases. It means that only two parameters (sample mean of EEG Euclidean distances at a given time lag and relevant coefficient of variation) may be used in the approximate classification of empirical pdf's. Both these parameters tend to increase in the first twenty years of life and tend to decrease as healthy adults getting older. Our findings indicate that such age-related dependence of these parameters looks like as agerelated dependence of the total brain white matter volume. It is shown that 15 min hypoxia (8% oxygen in nitrogen) causes a significant (about 50%) decrease of the mean relative displacement EEG value that is typical for the rest state. In some sense the impact of the oxygen deficit looks like the subject getting older during short-term period.

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Recent Developments in Nonparametric Density Estimation

Cited by 348 publications

References 160 publications

The Acs Fornax Cluster Survey. Viii. The Luminosity Function of Globular Clusters in Virgo and Fornax Early-Type Galaxies and Its Use as a Distance Indicator

The Acs Fornax Cluster Survey. Viii. The Luminosity Function of Globular Clusters in Virgo and Fornax Early-Type Galaxies and Its Use as a Distance Indicator

Uncertainty propagation of arbitrary probability density functions applied to upscaling of transmissivities

Age-Related Changes in Probability Density Function of Pairwise Euclidean Distances between Multichannel Human EEG Signals

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