On the histogram as a density estimator:L2 theory

By David Freedman, Persi Diaconis. 1981

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Citations in the corpus

Auditing black-box models for indirect influence (2016, methodology): “Bins are chosen using the Freedman-Diaconis rule for choosing histogram bin sizes [11].”
Differential privacy and robust statistics (2009, background): “The interquartile range (IQR) [8] is a well-known robust estimate for the scale of the data.”
Dimensions and their poles: A metric and topological approach to opposites (2011, background): “…wider than g is based on the number of bins we tend assign to g (Ng) and to g (Ng); leading us to partition Simple Freedman & Diaconis case labelled ‘‘Freedman and Diaconis (1981)’’, N n1=3R 2 IQR ; where is the symbol for the floor operation, n is the number of observations, R is the range of X,…”
Protein Sectors: Statistical Coupling Analysis versus Conservation (2014, unknown): “an artifact of the fact that Reynolds et al. applied a constant threshold to histogram values instead of PDF values, and the bin size for the histograms was determined using the FreedmanDiaconis rule [38], and thus varied between eigenvectors. This can be seen from the Matlab scripts provided by the”
How many bins should be put in a regular histogram (2006, methodology): “Such evaluations have been made by Scott [22] and Freedman and Diaconis [11] for the squared L2-loss, by Devroye and Györfi [9] for the L1-loss and by Kanazawa [17] for the squared Hellinger distance.”
Entropy Inference and the James-Stein Estimator, with Application to Nonlinear Gene Association Networks (2008, methodology): “If the data are not already discretized, we propose employing the simple algorithm of Freedman and Diaconis (1981), considering the measurements of all genes simultaneously.”
Matching for Causal Inference Without Balance Checking (2008, unknown): “5 √ s̄nn −1/3 (Scott, 1992), and Freedman and Diaconis (1981) ∆fd = 2(Q3 −Q1)n.”
Computational Statistics Handbook with MATLAB (2001, methodology): “Friedman [1987] combines steepest-ascent with a stepping search to look for a region of interest. Crawford [1991] uses genetic algorithms to optimize the projection index.”
Do Hedge Fund Managers Misreport Returns? Evidence from the Pooled Distribution (2009, unknown): “In practical applications, the most popular choices are derived by Scott (1979), Freedman and Diaconis (1981), and Silverman (1986).”
Precision luminosity measurements at LHCb (2014, background): “6 The bin width is determined as two times the interquartile range (the difference between the 75 and the 25 percentiles) divided by the number of observations in the sample to the power of 1/3 [45].”
Communication-Efficient Distributed Learning of Discrete Probability Distributions (2017, methodology): “In statistics, many methods have been proposed to estimate histogram distributions in a variety of settings [22, 34, 17, 31].”
Auditing Black-box Models by Obscuring Features (2016, methodology): “Bins are chosen according to the Freedman-Diaconis rule, used for choosing histogram bin sizes [7].”
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).”
Distribution-Free Learning of Bayesian Network Structure in Continuous Domains (2005, methodology): “'s method (Freedman & Diaconis 1981) is an improvement over Scott's method intended to be more robust to outliers.”