modeest {modeest}

Mode Estimation

Description

This package provides 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().

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 note on the estimation of the mode. Ann. Math. Statist., 42(6):1909-1915.

• Yamato H. (1971). 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). 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). Estimation of a multivariate mode. Ann. Statist., 6:802-812.

• Devroye L. (1979). Recursive estimation of the mode of a multivariate density. Canadian J. Statist., 7(2):159-167.

• Sager T.W. (1979). 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.

• Vieu P. (1996). A note on density mode estimation. Statistics \& Probability Letters, 26:297–307.

• 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.

• Leclerc J. (2000). Strong limiting behavior of two estimates of the mode: the shorth and the naive estimator. Statistics and Decisions, 18(4).

• 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.

• 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. and Pelletier M. (2005). Adaptive Estimation of the Mode of a Multivariate Density. J. Nonparametr. Statist., 17(1):83-105.

• Bickel D.R. and 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.