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modeest (version 1.09)

modeest: Mode Estimation

Description

This package intends to provide estimators of the mode of univariate unimodal (and sometimes multimodal) data and values of the modes of usual probability distributions. For a complete list of functions, use library(help = "modeest") or help.start().

Arguments

Details

ll{ Package: modeest Type: Package Version: 1.09 Date: 2009-05-23 License: GPL version 2 or newer }

References

  • Parzen E. (1962). On estimation of a probability density function and mode.Ann. Math. Stat.,33(3):1065-1076.
  • Chernoff H. (1964). Estimation of the mode.Ann. Inst. Statist. Math.,16:31-41.
  • Huber P.J. (1964). Robust estimation of a location parameter.Ann. Math. Statist.,35:73-101.
  • Dalenius T. (1965). The Mode - A Negleted Statistical Parameter.J. Royal Statist. Soc. A,128:110-117.
  • Grenander U. (1965). Some direct estimates of the mode.Ann. Math. Statist.,36:131-138.
  • Venter J.H. (1967). On estimation of the mode.Ann. Math. Statist.,38(5):1446-1455.
  • Lientz B.P. (1969). On estimating points of local maxima and minima of density functions.Nonparametric Techniques in Statistical Inference (ed. M.L. Puri, Cambridge University Press), p.275-282.
  • Lientz B.P. (1970). Results on nonparametric modal intervals.SIAM J. Appl. Math.,19:356-366.
  • Wegman E.J. (1971). % a revoir !! A note on the estimation of the mode.Ann. Math. Statist.,42(6):1909-1915.
  • Yamato H. (1971). % a revoir !! Sequential estimation of a continuous probability density function and mode.Bull. Math. Statist.,14:1-12.
  • Ekblom H. (1972). A Monte Carlo investigation of mode estimators in small samples.Applied Statistics,21:177-184.
  • Lientz B.P. (1972). Properties of modal intervals.SIAM J. Appl. Math.,23:1-5.
  • Konakov V.D. (1973). On the asymptotic normality of the mode of multidimensional distributions.Theory Probab. Appl.,18:794-803.
  • Robertson T. and Cryer J.D. (1974). An iterative procedure for estimating the mode.J. Amer. Statist. Assoc.,69(348):1012-1016.
  • Kim B.K. and Van Ryzin J. (1975). Uniform consistency of a histogram density estimator and modal estimation.Commun. Statist.,4:303-315.
  • Sager T.W. (1975). % a revoir !! Consistency in nonparametric estimation of the mode.Ann. Statist.,3(3):698-706.
  • Stone C.J. (1975). Adaptive maximum likelihood estimators of a location parameter.Ann. Statist.,3:267-284.
  • Mizoguchi R. and Shimura M. (1976). Nonparametric Learning Without a Teacher Based on Mode Estimation.IEEE Transactions on Computers,C25(11):1109-1117.
  • Adriano K.N., Gentle J.E. and Sposito V.A. (1977). On the asymptotic bias of Grenander's mode estimator.Commun. Statist.-Theor. Meth. A,6:773-776.
  • Asselin de Beauville J.-P. (1978). Estimation non parametrique de la densite et du mode, exemple de la distribution Gamma.Revue de Statistique Appliquee,26(3):47-70.
  • Sager T.W. (1978). % a revoir !! Estimation of a multivariate mode.Ann. Statist.,6:802-812.
  • Devroye L. (1979). % a revoir !! Recursive estimation of the mode of a multivariate density.Canadian J. Statist.,7(2):159-167.
  • Sager T.W. (1979). % a revoir !! An iterative procedure for estimating a multivariate mode and isopleth.J. Amer. Statist. Assoc.,74(366):329-339.
  • Eddy W.F. (1980). Optimum kernel estimators of the mode.Ann. Statist.,8(4):870-882.
  • Eddy W.F. (1982). The Asymptotic Distributions of Kernel Estimators of the Mode.Z. Wahrsch. Verw. Gebiete,59:279-290.
  • Hall P. (1982). Asymptotic Theory of Grenander's Mode Estimator.Z. Wahrsch. Verw. Gebiete,60:315-334.
  • Sager T.W. (1983). Estimating modes and isopleths.Commun. Statist.-Theor. Meth.,12(5):529-557.
  • Hartigan J.A. and Hartigan P.M. (1985). The Dip Test of Unimodality.Ann. Statist.,13:70-84.
  • Hartigan P.M. (1985). Computation of the Dip Statistic to Test for Unimodality.Appl. Statist. (JRSS C),34:320-325.
  • Romano J.P. (1988). On weak convergence and optimality of kernel density estimates of the mode.Ann. Statist.,16(2):629-647.
  • Tsybakov A. (1990). Recursive estimation of the mode of a multivariate distribution.Probl. Inf. Transm.,26:31-37.
  • Hyndman R.J. (1996). Computing and graphing highest density regions.Amer. Statist.,50(2):120-126.
  • Leclerc J. (1997). Comportement limite fort de deux estimateurs du mode : le shorth et l'estimateur naif.C. R. Acad. Sci. Paris, Serie I,325(11):1207-1210. %\item Minnotte M. C. (1997). %Nonparametric testing of the existence of modes. %\emph{Ann. Statist.}, \bold{25}(4):1646-1660. % %\item Futschik A. (1999). %A new estimate of the mode based on the quantile density. %\emph{Statistics and Probability Letters}, \bold{43}:145-152. %
  • Leclerc J. (2000). Strong limiting behavior of two estimates of the mode: the shorth and the naive estimator.Statistics and Decisions,18(4).
  • Groeneboom P.and Wellner J.A. (2001). Computing Chernoff's distribution.J. Comput. Graph. Statist.,10:388-400.
  • Shoung J.M. and Zhang C.H. (2001). Least squares estimators of the mode of a unimodal regression function.Ann. Statist.,29(3):648-665.
  • Bickel D.R. (2002). Robust estimators of the mode and skewness of continuous data.Computational Statistics and Data Analysis,39:153-163.
  • Abraham C., Biau G. and Cadre B. (2003). Simple Estimation of the Mode of a Multivariate Density.Canad. J. Statist.,31(1):23-34.
  • Bickel D.R. (2003). Robust and efficient estimation of the mode of continuous data: The mode as a viable measure of central tendency.J. Statist. Comput. Simul.,73:899-912.
  • Djeddour K., Mokkadem A. et Pelletier M. (2003). Sur l'estimation recursive du mode et de la valeur modale d'une densite de probabilite.Technical report 105.
  • Djeddour K., Mokkadem A. et Pelletier M. (2003). Application du principe de moyennisation a l'estimation recursive du mode et de la valeur modale d'une densite de probabilite.Technical report 106.
  • Hedges S.B. and Shah P. (2003). Comparison of mode estimation methods and application in molecular clock analysis.BMC Bioinformatics,4:31-41. %\item Ziegler K. (2003). %On the asymptotic normality of kernel regression estimators of the mode in the nonparametric random design model. %\emph{Journal of Statistical Planning and Inference}, \bold{115}:123-144.
  • Herrmann E. and Ziegler K. (2004). Rates of consistency for nonparametric estimation of the mode in absence of smoothness assumptions.Statistics and Probability Letters,68:359-368.
  • Abraham C., Biau G. and Cadre B. (2004). On the Asymptotic Properties of a Simple Estimate of the Mode.ESAIM Probab. Stat.,8:1-11.
  • Mokkadem A. et Pelletier M. (2005). Adaptive Estimation of the Mode of a Multivariate Density.J. Nonparametr. Statist.,17(1):83-105.
  • Bickel D.R. et Fruehwirth R. (2006). On a Fast, Robust Estimator of the Mode: Comparisons to Other Robust Estimators with Applications.Computational Statistics and Data Analysis,50(12):3500-3530.

See Also

mlv for general mode estimation