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This tutorial provides a gentle introduction to kernel density estimation (KDE) and recent advances regarding confidence bands and geometric/topological features.
Relations between the critical points of a real function of n independent variables
M. Morse · 1925
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Asymptotic theory for density ridges
Y.-C. Chen, C. R. Genovese, and L. Wasserman · 1928
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The foundations of a theory of the calculus of variations in the large in m-space (second paper)
M. Morse · 1930
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On estimation of a probability density function and mode
E. Parzen · 1962
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Some new estimates for distribution functions
E. A. Nadaraya · 1964
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A nonparametric estimate of a multivariate density function
D. O. Loftsgaarden and C. P. Quesenberry · 1965
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On choosing a delta-sequence
M. Woodroofe · 1970
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On some global measures of the deviations of density function estimates
P. Bickel and M. Rosenblatt · 1973
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Strong uniform consistency of integrals of density estimators
B. Winter · 1973
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The estimation of the gradient of a density function, with applications in pattern recognition
K. Fukunaga and L. Hostetler · 1975
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On the maximal deviation of k k -dimensional density estimates
M. Rosenblatt et al · 1976
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Variable kernel estimates of multivariate densities
L. Breiman, W. Meisel, and E. Purcell · 1977
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Bootstrap methods: Another look at the jackknife
B. Efron · 1979
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A note on the estimation of a distribution function and quantiles by a kernel method
A. Azzalini · 1981
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Nonparametric estimation of smooth distribution functions
R.-D. Reiss · 1981
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Empirical choice of histograms and kernel density estimators
M. Rudemo · 1982
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Optimal global rates of convergence for nonparametric regression
C. J. Stone · 1982
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An alternative method of cross-validation for the smoothing of density estimates
A. Bowman · 1984
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Remarks on some smoothed empirical distribution functions and process
Y. Mack · 1984
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Statistical approaches to the analysis of receiver operating characteristic (roc) curves
B. J. McNeil and J. A. Hanley · 1984
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An asymptotically optimal window selection rule for kernel density estimates
C. J. Stone · 1984
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Uniform confidence bounds for regression based on a simple moving average
S. Bjerve, K. A. Doksum, and B. S. Yandell · 1985
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Comparison of receiver operating curves derived from the same population: a bootstrapping approach
A. Moise, B. Clément, P. Ducimetière, and M. G. Bourassa · 1985
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Laws of large numbers for classes of functions
J. Yukich · 1985
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On the bootstrap and confidence intervals
P. Hall · 1986
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Density Estimation for Statistics and Data Analysis
B. W. Silverman · 1986
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Prepivoting to reduce level error of confidence sets
R. Beran · 1987
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Calibrating confidence coefficients
W.-Y. Loh · 1987
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Biased and unbiased cross-validation in density estimation
D. W. Scott and G. R. Terrell · 1987
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Bootstrapping in nonparametric regression: local adaptive smoothing and confidence bands
W. Härdle and A. W. Bowman · 1988
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Almost sure convergence of smoothed empirical distribution functions
L. T. Fernholz · 1991
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On convergence rates of suprema
P. Hall · 1991
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Bootstrap simultaneous error bars for nonparametric regression
W. Hardle and J. Marron · 1991
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A reliable data-based bandwidth selection method for kernel density estimation
S. Sheather and C. Jones · 1991
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Variable kernel density estimation
G. R. Terrell and D. W. Scott · 1992
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Weak convergence of smoothed empirical processes
J. Yukich · 1992
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Confidence bands in nonparametric regression
R. L. Eubank and P. L. Speckman · 1993
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Empirical likelihood confidence bands in density estimation
P. Hall and A. B. Owen · 1993
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Smoothing bias in density derivative estimation
T. M. Stoker · 1993
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Advances in statistical methodology for the evaluation of diagnostic and laboratory tests
G. Campbell · 1994
Cited alongside, same era.
Simultaneous confidence bands for linear regression and smoothing
J. Sun and C. R. Loader · 1994
Cited alongside, same era.
Mean shift, mode seeking, and clustering
Y. Cheng · 1995
Cited alongside, same era.
Better bootstrap confidence intervals for regression curve estimation
W. Härdle, S. Huet, and E. Jolivet · 1995
Cited alongside, same era.
Automatic bandwidth choice and confidence intervals in nonparametric regression
M. H. Neumann · 1995
Cited alongside, same era.
Measuring mass concentrations and estimating density contour clusters-an excess mass approach
W. Polonik · 1995
Cited alongside, same era.
Introduction to nonparametric estimation. revised and extended from the 2004 french original. translated by vladimir zaiats, 2009
A. B. Tsybakov · 2009
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Visual exploration of high dimensional scalar functions
S. Gerber, P.-T. Bremer, V. Pascucci, and R. Whitaker · 2010
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Generalized density clustering
A. Rinaldo and L. Wasserman · 2010
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Asymptotics for general multivariate kernel density derivative estimators
J. E. Chacón, T. Duong, and M. Wand · 2011
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Density estimation in r
H. Deng and H. Wickham · 2011
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Data analysis with the morse-smale complex: The msr package for r
S. Gerber and K. Potter · 2011
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Empirical likelihood confidence intervals for nonparametric density estimation
S. X. Chen · 1996
Cited alongside, same era.
Nonparametric and semiparametric estimation of the receiver operating characteristic curve
F. Hsieh, B. W. Turnbull, et al · 1996
Cited alongside, same era.
A brief survey of bandwidth selection for density estimation
M. C. Jones, J. S. Marron, and S. J. Sheather · 1996
Cited alongside, same era.
Applied smoothing techniques for data analysis: the kernel approach with S-Plus illustrations , volume 18
A. W. Bowman and A. Azzalini · 1997
Cited alongside, same era.
On nonparametric estimation of density level sets
A. B. Tsybakov · 1997
Cited alongside, same era.
Smooth non-parametric receiver operating characteristic (roc) curves for continuous diagnostic tests
K. H. Zou, W. Hall, and D. E. Shapiro · 1997
Cited alongside, same era.
Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality
A. Goldenshluger and O. Lepski · 2011
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Locally defined principal curves and surfaces
U. Ozertem and D. Erdogmus · 2011
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Confidence intervals and bands for the binormal roc curve revisited
E. Demidenko · 2012
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Persistent homology: theory and practice
H. Edelsbrunner and D. Morozov · 2012
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Stability of density-based clustering
A. Rinaldo, A. Singh, R. Nugent, and L. Wasserman · 2012
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Cluster trees on manifolds
S. Balakrishnan, S. Narayanan, A. Rinaldo, A. Singh, and L. Wasserman · 2013
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Data-driven density derivative estimation, with applications to nonparametric clustering and bump hunting
J. E. Chacón and T. Duong · 2013
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Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors
V. Chernozhukov, D. Chetverikov, and K. Kato · 2013
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Morse–smale regression
S. Gerber, O. Rübel, P.-T. Bremer, V. Pascucci, and R. T. Whitaker · 2013
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A simple bootstrap method for constructing nonparametric confidence bands for functions
P. Hall and J. Horowitz · 2013
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Consistent tests for conditional treatment effects
Y.-C. Hsu · 2013
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Confidence regions for level sets
E. Mammen and W. Polonik · 2013
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Consistent procedures for cluster tree estimation and pruning
K. Chaudhuri, S. Dasgupta, S. Kpotufe, and U. von Luxburg · 2014
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Robust topological inference: Distance to a measure and kernel distance
F. Chazal, B. T. Fasy, F. Lecci, B. Michel, A. Rinaldo, and L. Wasserman · 2014
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Confidence sets for persistence diagrams
B. T. Fasy, F. Lecci, A. Rinaldo, L. Wasserman, S. Balakrishnan, and A. Singh · 2014
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Nonparametric ridge estimation
C. R. Genovese, M. Perone-Pacifico, I. Verdinelli, and L. Wasserman · 2014
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Treatment selection in a randomized clinical trial via covariate-specific treatment effect curves
Y. Ma and X.-H. Zhou · 2014
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Nonparametric functional estimation
B. P. Rao · 2014
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Estimating conditional average treatment effects
J. Abrevaya, Y.-C. Hsu, and R. P. Lieli · 2015
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Risk bounds for mode clustering
M. Azizyan, Y.-C. Chen, A. Singh, and L. Wasserman · 2015
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On the effect of bias estimation on coverage accuracy in nonparametric inference
S. Calonico, M. D. Cattaneo, and M. H. Farrell · 2015
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A population background for nonparametric density-based clustering
J. E. Chacón et al · 2015
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Beyond hartigan consistency: Merge distortion metric for hierarchical clustering
J. Eldridge, M. Belkin, and Y. Wang · 2015
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Multivariate density estimation: theory, practice, and visualization
D. W. Scott · 2015
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On the estimation of the gradient lines of a density and the consistency of the mean-shift algorithm
E. Arias-Castro, D. Mason, and B. Pelletier · 2016
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Generalized cluster trees and singular measures
Y.-C. Chen · 2016
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A comprehensive approach to mode clustering
Y.-C. Chen, C. R. Genovese, and L. Wasserman · 2016
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Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related gaussian couplings
V. Chernozhukov, D. Chetverikov, and K. Kato · 2016
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Statistical inference for cluster trees
K. Jisu, Y.-C. Chen, S. Balakrishnan, A. Rinaldo, and L. Wasserman · 2016
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Theoretical analysis of nonparametric filament estimation
W. Qiao, W. Polonik, et al · 2016
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L. Wasserman · 2016
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Nonparametric inference via bootstrapping the debiased estimator
Y.-C. Chen · 2017
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