On Bandwidth Variation in Kernel Estimates-A Square Root Law

By Ian Abramson. 1982

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

One-Class Support Measure Machines for Group Anomaly Detection (2013, background): “n ν = 1 as a generalization of traditional KDE, where we have a data-dependent bandwidth at each data point. This type of KDE is known in the statistics as variable kernel density estimators (VKDEs) (Abramson 1982, Breiman et al. 1977, Terrell and Scott 1992). For ν < 1, the OCSMM gives a sparse ”
Robust kernel density estimation (2008, methodology): “or. The VKDE has a variable bandwidth for each data point, fb VKDE(x) = 1 n Xn i=1 k ˙ i (x;X i); and the bandwidth ˙ iis set as ˙ i= ˙ fb KDE(X i) 1=2 where is the mean of ffb KDE(X i)gn i=1 (Abramson, 1982; Comaniciu et al., 2001). There is another implementation of the VKDE where ˙ iis based o”
Local Multiplicative Bias Correction for Asymmetric Kernel Density Estimators (2007, background): “Bias 3 f̃ b (x) ́ = f0 (x) ∙ {r((1)) 0 (x)− r((1))(x, θ2)}+ 1 2 x{r((2)) 0 (x)− r((2))(x, θ2)} ̧ b”
Nonlinear Granger Causality: Guidelines for Multivariate Analysis (2013, unknown): “The literature distinguishes inter alia among higher order kernels (Granovsky and Mller, 1991), variable bandwith estimators (Abramson, 1982), variable location estimators (Samiuddin and El-Sayyad, 1990) or parametric transformation methods (Abramson, 1984).”
Variable Bandwidth and Local Linear Regression (1991, background): “Further related studies can be found in Abramson (1982), Hall and Marron (1988), Hall (1990) and Jones (1990).”
Kernel Regression for Image Processing and Reconstruction (2007, background): “4In this paper, we choose = 0:5, which is proved in [34] to be an appropriate overall choice for the density sensitivity parameter.”
Shift Restrictions and Semiparametric Estimation in Ordered Response Models (2002, methodology): “The kernel density estimators are defined in D1 through D3 using local smoothing techniques for bias reduction developed by Abramson (1982) and Silverman (1986).”
Kernel bandwidth optimization in spike rate estimation (2009, methodology): “Abramson’s adaptive kernel method (Abramson 1982) uses the sample point kernel estimate ˆ λ t = (cid:24) i k w ti ( t − t i ) , in which the bandwidths are adapted between the underlying and estimated rate.”
An R package for statistical provenance analysis (2016, methodology): “…scale with the square root of the local density, normalised by the geometric mean of the entire al data. a. the CAD of sample N1; b. the KDE of sample N1, using a the hybrid adaptive bandwidth of 50 Ma and a log scale; d. the quartz—feldspar—lithic composition of the distribution (Abramson, 1982).”
The Generalized Cross Entropy Method, with Applications to Probability Density Estimation (2011, unknown): “, [14], [39], [37], [52], [35], [59], [1]).”
Variable bandwidth and one-step local M-estimator (2000, background): “(A8) The function 0( ) satis es that E[ sup jzj j 0("+ z) 0(")j jX = x] = o(1) and E[ sup jzj j ("+ z) (") 0(")zj jX = x] = o( ); as ! 0; uniformly in x in a neighborhood of x0 The conditions above are mild and are ful lled in many applications.”
Family of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data (2015, methodology): “For (ii), adaptive smoothing such as variable bandwidth methods (e.g. Abramson 1982) would be a remedy.”
IsoplotR: A free and open toolbox for geochronology (2018, methodology): “The default bandwidth used by IsoplotR is calculated using the algorithm of Botev et al. (2010) and modulated by the adaptive smoothing approach of Abramson (1982), whereby: hi ¼ h ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi G=kdeðtiÞ q in which kde(ti) is the ‘pilot density’ using…”