Kernel density estimation using weighted data^∗

Bandwidth selection for kernel density estimation with length-biased data

“…Another extensions using Fourier series have been proposed in Jones and Karunamuni (1997). Later a third non-parametric estimator has been considered in Guillamón et al (1998). Density estimation for weighted data has also been studied from other points of view, Barmi and Simonoff (2000) proposed a simple transformation-based approach motivated by the form of the non-parametric maximun likelihood estimator of the density.…”

Transformation- based density estimation For weighted distributions

“…Jones (1991) demonstrated good properties of the estimate compared to an earlier proposal of Bhattacharyya, Franklin and Richardson (1988). Further discussion of kernel-type estimation for weighted distributions can be found in Richardson, Kazempour and Bhattacharyya (1991); Ahmad (1995); Wu and Mao (1996); Wu (1997a,b) and Guillamon, Navarro and Ruiz (1998).…”

Learning In Spike Trains: Estimating Within-Session Changes In Firing Rate Using Weighted Interpolation

“…When h = 1, this corresponds to ordinary kernel density estimation. When h > 1, the observed spikes differ in their weights, requiring a weighted kernel density estimate to be computed (Guillamón et al, 1998). In either case, this permits rapid approximation of the corresponding GCV scores: When values of h, h r , and h s are selected based on optimizing box kernel estimates rather than ARRIS estimates, they respond to the same general features of the data that ARRIS would respond to.…”