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modeest (version 1.06)

modeest: Mode Estimation - Chernoff Distribution

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. It also includes computation of the density function, distribution function, and quantile function of the Chernoff distribution, which is the limiting distribution of the Chernoff mode estimator. For a complete list of functions, use library(help = "modeest") or help.start().

Arguments

Details

ll{ Package: modeest Type: Package Version: 1.03 Date: 2006-12-01 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). % � revoir !! A note on the estimation of the mode.Ann. Math. Statist.,42(6):1909-1915.
  • Yamato H. (1971). % � 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). % � 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 param�trique de la densit� et du mode, exemple de la distribution Gamma.Revue de Statistique Appliqu�e,26(3):47-70.
  • Sager T.W. (1978). % � revoir !! Estimation of a multivariate mode.Ann. Statist.,6:802-812.
  • Devroye L. (1979). % � revoir !! Recursive estimation of the mode of a multivariate density.Canadian J. Statist.,7(2):159-167.
  • Sager T.W. (1979). % � 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 na�f.C. R. Acad. Sci. Paris, S�rie 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 r�cursive du mode et de la valeur modale d'une densit� de probabilit�.Technical report 105.
  • Djeddour K., Mokkadem A. et Pelletier M. (2003). Application du principe de moyennisation � l'estimation r�cursive du mode et de la valeur modale d'une densit� de probabilit�.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 Fr�hwirth 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; dchern for the Chernoff distribution