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The Gram-Charlier A Series based Extended Rule-of-Thumb for Bandwidth Selection in Univariate and Multivariate Kernel Density Estimations [article]

Dharmani Bhaveshkumar C
2015 arXiv   pre-print
The article derives a novel Gram-Charlier A (GCA) Series based Extended Rule-of-Thumb (ExROT) for bandwidth selection in Kernel Density Estimation (KDE).  ...  Intuitively, better estimation of R(f"(·)) and consequently better bandwidth selection rules can be derived, if the unknown PDF is approximated through an infinite series expansion based on a more generalized  ...  Then, the bandwidth selection rule in Equation (37) 4! Over all, the Gram-Charlier A Series based Extended Rule-of-Thumb for bandwidth parameter h GC selection in multivariate KDE is obtained.  ... 
arXiv:1504.00781v1 fatcat:ng6bic3pbjfdvgvhakbgu3fd34

Gradient of Probability Density Functions based Contrasts for Blind Source Separation (BSS) [article]

Dharmani Bhaveshkumar C
2015 arXiv   pre-print
Instead of a conventional two stage indirect estimation method for joint PDF based BSS contrast estimation, a single stage direct estimation of the contrasts is desired.  ...  For the k^th order differentiable multivariate functions with equal hyper-volumes (region bounded by hyper-surfaces) and with a constraint of bounded support for k>1, it proves that equality of any k^th  ...  The suitable choice of a kernel bandwidth parameter using data dependent bandwidth selection Extended Rule-of-Thumb by (Dharmani Bhaveshkumar, 2015) achieves a parameter free contrast estimation.  ... 
arXiv:1504.02712v1 fatcat:zfkkm7fk3vemxf4gf7pupenela

Semiparametric maximum likelihood probability density estimation

Frank Kwasniok, Bryan C Daniels
2021 PLoS ONE  
The new technique compares very favourably to kernel density estimation, the diffusion estimator, finite mixture models and local likelihood density estimation across a diverse range of simulation and  ...  The semiparametric estimator combines a very small mean integrated squared error with a high degree of smoothness which allows for a robust and reliable detection of the modality of the probability density  ...  Acronym Description KDE1 Gaussian kernel density estimator with rule-of-thumb bandwidth [1] ; reflection method applied at any boundary point KDE2 MATLAB in-built Gaussian kernel density estimator with  ... 
doi:10.1371/journal.pone.0259111 pmid:34752460 pmcid:PMC8577774 fatcat:5d3za43znvgfjl2yznkjmys26i

Applied Multivariate Statistical Analysis

Charles E Heckler
2005 Technometrics  
Summary → Kernel densities estimate distribution densities by the kernel method. → The bandwidth h determines the degree of smoothness of the estimate f . → Kernel densities are smooth functions and they  ...  This bandwidth is to be used only in combination with a Gaussian kernel ϕ. → Kernel density estimates are a good descriptive tool for seeing modes, location, skewness, tails, asymmetry, etc.  ...  The canonical correlation analysis is a standard tool of multivariate statistical analysis for discovery and quantification of associations between two sets of variables.  ... 
doi:10.1198/tech.2005.s319 fatcat:2mbwm76nsrd35k7ymm5opxq2he

Some problems in testing for modality [article]

Matthew Gerard York, University, The Australian National, University, The Australian National
,a m). See Johnson and Kotz (1970, Section 4.2) for an account of Gram-Charlier expansion.  ...  More recent bandwidth selection rules have employed "plug-in" ideas.  ...  Density Densit  ... 
doi:10.25911/5d778921d31f1 fatcat:vlwld4yairgg5fbn5vl6we62zy