An alternative method of cross-validation for the smoothing of density estimates

By Adrian W. Bowman. 1984

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

Kernel Bayes' Rule (2010, methodology): “-component of V . The sample sizes were n = ℓ = 200. The bandwidth parameters hX,hY in KDE were set hX = hY , and chosen over the set {2 ∗ i | i = 1,...,10} in two ways: least square cross-validation [5, 27] and the best mean performance. For the KBR, we chose σ in e−kx−x′k2/(2σ2) in two ways: the m”
Self‐consistent method for density estimation (2009, methodology): “.g. varying the cutoﬀ parameter in MPL and Field Theory precisely corresponds to diﬀerent choices of the bayesian prior [2]). Cross-validation techniques have been previously applied for this purpose [4], but they are computationally expensive and have been seldom applied in the literature. In this ”
Testing for Spatial Autocorrelation among the Residuals of the Geographically Weighted Regression (2000, methodology): “A cross-validation procedure (for example, see Bowman,1984; Cleveland,1979) is used for this purpose.”
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).”
Bayesian Inference and Model Assessment for Spatial Point Patterns Using Posterior Predictive Samples (2017, methodology): “Diggle and Marron (1988) adapted leave-one-out cross-validation from Bowman (1984) for bandwidth selection for kernel intensity estimates. For a Bayesian approach where MCMC model fitting is needed, the computational burden required for leave-oneout cross-validation is impractical. However, we can e”
Statistical Tests for Spatial Nonstationarity Based on the Geographically Weighted Regression Model (2000, methodology): “This can be done by a cross-validation procedure (for example, see Cleveland, 1979; Bowman, 1984; Brunsdon, 1995).”
A Review on Modal Clustering (2016, methodology): “…multivariate generalisation of the plug-in rule introduced by Wand & Jones (1994), HPI; (ii) a least square cross-validation selector (multivariate generalisation of Bowman, 1984), HCV; and (iii) the asymptotically optimal International Statistical Review (2016), 84, 3, 413–433 © 2015 The Authors.”
Nonparametric density estimation for multivariate bounded data (2007, methodology): “For the Gaussian kernel estimator, its consistency is investigated by Rudemo (1982), Hall (1983), Stone (1984), Bowman (1984), Härlde and Marron (1985), and Marron and Härlde (1986). In this section, we show the performance of the LSCV method for the product kernel estimator based on the gamma kerne”
GWmodel: An R Package for Exploring Spatial Heterogeneity Using Geographically Weighted Models (2013, methodology): “An optimum kernel bandwidth for GW regression can be found by minimising some model fit diagnostic, such as a leave-one-out cross-validation (CV) score (Bowman 1984), which only accounts for model prediction accuracy; or the Akaike Information Criterion (AIC) (Akaike 1973), which accounts for model ”
Indirect Cross-Validation for Density Estimation (2008, methodology): “The two most widely used are least-squares crossvalidation, proposed independently by Rudemo (1982) and Bowman (1984) and the Sheather and Jones (1991) plug-in method.”
Multivariate plug-in bandwidth selection with unconstrained pilot bandwidth matrices (2010, background): “Unbiased cross validation selectors (Rudemo 1982; Bowman 1984) and biased cross validation selectors (Scott and Terrell 1987; Sain et al.”
Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data (2014, methodology): “…bandwidth can be found by minimising some model goodness-of-fit diagnostic (Loader 1999), such as the cross-validation (CV) score (Cleveland 1979, Bowman 1984), which only accounts for model prediction accuracy, or the Akaike Information Criterion (AIC) (Akaike 1973), which accounts for model…”
A tutorial on kernel density estimation and recent advances (2017, methodology): “Common approaches to bandwidth selection include the rule of thumb (Silverman, 1986), least square cross-validation, (Rudemo, 1982; Bowman, 1984; Bowman and Azzalini, 1997; Stone, 1984), biased cross-validation, (Scott and Terrell, 1987), and plug-in method (Woodroofe, 1970; Sheather and Jones, 1991”
A nonparametric method for estimating asymmetric densities based on skewed Birnbaum–Saunders distributions applied to environmental data (2013, background): “A similar algorithm can be used for the optimal searching of g. (iii) The least squares cross validation (LSCV) method may be used to select the bandwidth h, which 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 no”