Probability Density Function Estimation Using Gamma Kernels

By Songxi Chen. 2000

385 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/63a0002ca72f6106e2019dd2dc4455769907a2f1

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In Artificial Intelligence

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes (2010, neutral): “Thus instead, we consider a gamma kernel estimator as proposed in Chen (2000) whose flexible form ensures that it is boundary bias free, while density estimates are always nonnegative.”
Optimal asymmetric kernels (2004, neutral): “Other successful applications of asymmetric kernels include Samiuddin and El-Sayyad (1990), Holiday (1995), Chen (1999, 2000), Scaillet (2001) and Fernandes and Scaillet (2002); where such kernels are shown to lead to desirable properties.”
Family of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data (2015, methodology): “Furthermore, as pointed out by Chen (2000) and Scaillet (2004), a unique feature of asymmetric kernel density estimators is that the variance coefficient decreases as x increases.”
Density estimation using inverse and reciprocal inverse Gaussian kernels (2004, methodology): “Recently Chen (2000) has proposed a nice way to circumvent the well known boundary bias or edge effect that appears in standard kernel density estimation. Boundary bias is due to weight allocation by the fixed symmetric kernel outside the density support when smoothing is carried out near the bounda”
A nonparametric method for estimating asymmetric densities based on skewed Birnbaum–Saunders distributions applied to environmental data (2013, methodology): “In general, the class of asymmetric kernel density estimators is boundary bias free and its bias is of order O(h); see Chen (1999, 2000).”
Nonparametric specification tests for conditional duration models (2005, background): “with bandwidth bn provides estimates that are consistent, nonnegative, boundary bias free, and achieve the optimal rate of convergence for the mean integrated error for any density function whose support is bounded from the origin (Bouezmarni and Scaillet, 2002; Chen, 2000).”
Interpolation of precipitation under topographic influence at different time scales (2013, neutral): “As precipitation amounts are positive, traditional symmetrical kernels are inappropriate; therefore, gamma kernels [Chen, 2000] were selected: gtj zð Þ ¼ 1 #I tj X i2I tjð Þ K z b tjð Þ þ1;b tjð Þ z xi; tj ð10Þ where Kz bþ1;b uð Þ ¼ uz=be u=b bz=bþ1G z=bþ 1ð Þ ð11Þ [59] The parameter b tj defines…”
A Family of Nonparametric Density Estimation Algorithms (2013, background): “A good choice is that of localized radial expansions, which depend on a single parameter: all the complexity of arbitrary, possibly convoluted probability densities can be built through the composition of such simple maps.”