Empirical Choice of Histograms and Kernel Density Estimators

By Mats Rudemo. 1982

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Citations in the corpus

Kernel Bayes' Rule (2010, methodology): “The bandwidth parameter hX , hY in KDE were sethX = hY and chosen by two ways, the least square cross-validation [15] and the best mean performance, over the set {2 ∗ i | i = 1, .”
A nonparametric method for estimating asymmetric densities based on skewed Birnbaum–Saunders distributions applied to environmental data (2013, background): “…chooses it by minimizing the cross validation criterion defined as LSCVðhÞ ¼ R1 0 bf 2h ðxÞdx ð2=nÞ Pn i¼1 bfh; iðxiÞ; where bfh is a nonnegative asymmetric kernel density estimate of bandwidth h and bfh; i the corresponding estimate without the ith observation; see Rudemo (1982) and Bowman (1984).”
Cross‐validation Bandwidth Matrices for Multivariate Kernel Density Estimation (2005, methodology): “All of the methods described above are direct extensions of techniques for univariate density estimation (see Rudemo (1982) and Bowman (1984) for univariate UCV, Scott & Terrell (1987) and Jones & Kappenman (1992) for univariate BCV and Hall et al. (1992) for univariate SCV).”
Near optimal thresholding estimation of a Poisson intensity on the real line (2008, methodology): “For instance, Rudemo [37] studied data-driven histogram and kernel estimates based on the cross-validation method.”
A comprehensive review of Value at Risk methodologies (2014, background): “the following studies: Abad and Benito (2012), Sener et al. (2012), Chen et al.”
Fourier analysis of irregularly spaced data on Rd (2007, methodology): “Here the bandwidth δ is selected to be 0.14 by least squares cross-validation, which is a popular criterion in kernel density estimation that was proposed by Rudemo (1982) and Bowman (1984) and validated theoretically by Hall (1983).”
Kernel bandwidth optimization in spike rate estimation (2009, methodology): “Although theories have been suggested for selecting the bandwidth, cross-validating with the data (Rudemo 1982; Bowman 1984; Silverman 1986; Scott and Terrell 1987; Scott 1992; Jones et al. 1996; Loader 1999a, b), individual researchers have mostly chosen bandwidth arbitrarily.”
Bivariate frequency analysis of floods using a diffusion based kernel density estimator (2013, methodology): “A few typical methods for selecting the bandwidth include maximum likelihood cross validation [e.g., Duin, 1976], least-squares cross validation [Rudemo, 1982], and asymptotic mean integrated squared error [Reiss, 1981; Ghosh and Huang, 1992; Sain et al., 1994].”
Kernel Bayes' rule: Bayesian inference with positive definite kernels (2013, methodology): “The bandwidth parameters h X , h Y in KDE were set h X = h Y , and chosen over the set {2 * i | i = 1, . . . , 10} in two ways: least squares cross-validation (Rudemo, 1982; Bowman, 1984) and the best mean performance.”
Density Estimation (2004, unknown): “Rudemo (1982) proposed the same technique from a slightly different viewpoint.”
Statistical Methods for Distributional Analysis (2015, methodology): “For data represented by case A in Table 2 inference can be approached as for inference in the complete-information case with a redefined population: the limits of the support of the distribution (y, y) are replaced by the narrower truncation limits (z, z). If we wish to say more it may be possible t”
How many bins should be put in a regular histogram (2006, methodology): “An application to histograms and kernel estimators is given in Rudemo [21].”