On optimal and data based histograms

By David W. Scott. 1979

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Citations in the corpus

Nonparametric kernel estimators for image classification (2012, methodology): “Having the estimated kernel matrix (also called a Gram matrix), we then apply kernel classiﬁers such as SVM for classiﬁcation.”
Minimax Optimal Procedures for Locally Private Estimation (2016, background): “For higher degrees of smoothness ( β > 1), standard histogram estimators no longer achieve optimal rates in the classical setting (Scott 1979).”
Local Privacy and Minimax Bounds: Sharp Rates for Probability Estimation (2013, background): “For higher degrees of smoothness (β > 1), histogram estimators no longer achieve optimal rates in the classical setting [20].”
Noise Estimation Using Density Estimation for Self-Supervised Multimodal Learning (2020, methodology): “gories: (a) parametric or semiparametric approaches such as Gaussian Mixture models [57,1,16,40,90] and probabilistic graphical models [25,29,87]; and (b) non-parametric approaches such as histograms [65], Splines [72,9], neural network-based density estimation [38,31,79,80,78,54] and Kernel Density”
Robust global registration (2005, unknown): “3 , where σ f is the standard deviation of the N descriptor values [ Sco79 ].”
A ug 2 01 4 Local Privacy , Data Processing Inequalities , and Minimax Rates (2018, background): “3 Achievability by orthogonal projection estimators For higher degrees of smoothness (β > 1), standard histogram estimators no longer achieve optimal rates in the classical setting [47].”
Adaptive Hyper-box Matching for Interpretable Individualized Treatment Effect Estimation (2020, methodology): “Several rules have been developed to choose fixed-width bins based on the data (e.g., Scott 1979; Freedman and Diaconis 1981; Wand 1997).”
Regression analysis of variates observed on (0, 1): percentages, proportions and fractions (2003, methodology): “The number of bins for all histograms was determined using the method of Scott (1979).)”
Regional disparities in the European Union: Convergence and Agglomeration (2008, methodology): “Two approaches use the standard deviation and the number of cases to calculate class sizes (Devroye & Györfi, 1985; Scott, 1979).”
A Method for Selecting the Bin Size of a Time Histogram (2007, background): “It was proven that the optimal bin size scales as n − 1 / 3 with regard to the bar-graph-density estimator (R´ev´esz, 1968; Scott, 1979).”
Distribution-Free Learning of Bayesian Network Structure in Continuous Domains (2005, methodology): “• Scott's method (Scott 1979) dictates that the optimal bin width isˆh = 3.5ˆσN −1/(2+d) for multiple dimensions, wherê σ is the sample standard deviation and d is the number of dimensions.”
A Preliminary Appraisal of Seven Natural Zircon Reference Materials for In Situ Hf Isotope Determination (2005, methodology): “most efficient, unbiased estimate of the probability density function was determined using the method of Scott (1979).”
The 10,240‐member ensemble Kalman filtering with an intermediate AGCM (2014, methodology): “Here the Scott’s Choice method [Scott, 1979] is applied to find the appropriate bin width objectively.”
Estimation of Renyi Entropy and Mutual Information Based on Generalized Nearest-Neighbor Graphs (2010, methodology): “The number and the sizes of the bins were determined with the rule of Scott (1979).”
Multivariate extension of chi-squared univariate normality test (2010, background): “Even after the data become available, however, the choice of class intervals is still, in principle, a delicate issue with a large degree of arbitrariness involved and there is a large amount of literature on choosing the number of classes for any continuous distribution [1,2].”
REGO: Rank-based Estimation of Renyi Information using Euclidean Graph Optimization (2010, methodology): “We compared several estimators (k-NN, MST, k-MST, and the plug-in histogram estimator of Scott (1979)) with and without the empirical distributional transformation.”