Abstract
Kernel density estimators are useful building blocks for empirical statistical modeling of precipitation and other hydroclimatic variables. Data driven estimates of the marginal probability density function of these variables (which may have discrete or continuous arguments) provide a useful basis for Monte Carlo resampling and are also useful for posing and testing hypotheses (e.g bimodality) as to the frequency distributions of the variable. In this paper, some issues related to the selection and design of univariate kernel density estimators are reviewed. Some strategies for bandwidth and kernel selection are discussed in an applied context and recommendations for parameter selection are offered. This paper complements the nonparametric wet/dry spell resampling methodology presented in Lall et al. (1996).
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References
Abramson, I.S. 1982: On bandwidth variation in kernel estimates-a square root law, The Ann. of Statist. 10(4), 1217–1223
Bishop, Y.M.; Fienberg, S.E.; Holland, P.W. 1975: Discrete multivariate analysis: Theory and Practice, MIT Press, Cambridge, Mass
Chiu, S.-T. 1996: A comparative review of bandwidth selection for kernel density estimation, Statistica Sinica 6(1), 129–145
Coomans, D.; Broeckaert, I. 1986: Potential pattern recognition in chemical and medical decision making, John Wiley and sons, New York
Devroye, L.; Györfi, L. 1985: Nonparametric density estimation: The L1 view, John Wiley and Sons, New York
Dong Jianping; Simonoff, J. 1994: The construction and properties of boundary kernels for sparse multinomials, J. Computational and Graphical Statist. 3, 1–10
Epanechnikov, V.A. 1969: Nonparametric estimation of a multidimensional probability density, Theory of Probability and Applications 14, 153–158
Good, I.J.; Gaskins, R.A. 1971: Nonparametric roughness penalties for probability densities, Biometrika 58, 255–277
Hall, P.; Marron, J.S. 1987: Extent to which least-squares cross-validation minimizes integrated square error in nonparametric density estimation, Probability Theory Related Fields 74, 567–581
Hall, P.; Titterington, D.M. 1987: On smoothing sparse multinomial data, Australian J. Statist. 29(1), 19–37
Hand D.J. 1982: Kernel discriminant analysis, Pattern recognition and image processing research studies series, vol. 2, series Ed. J. Kittler, Research Studies press: Chichester
Härdle, W. 1991: Smoothing techniques with implementation in S, Springer Verlag, New York
Jones, M.C.; Marron, J.S.; Sheather, S.J. 1996: Progress in Data-Based Bandwidth Selection for Kernel Density Estimation, Computational Statist. 11 (3), 337–381
Lall, U.; Moon, Y.; Bosworth, K. 1993: Kernel flood frequency estimators: bandwidth selection and kernel choice, Water Resour. Res. 29(4), 1003–1015
Lall, U. 1995: Nonparametric function estimation: Recent hydrologic applications, US National report, 1991–1994, International Union of Geodesy and Geophysics, Review of Geophysics Supp., 1093–1102
Lall, U.; Rajagopalan, B.; Tarboton, D.G. 1996: A nonparametric wet/dry spell model for resampling daily precipitation, Water Resour. Res. 32(9), 2803–2823
Müller, H.G. 1988: Nonparametric regression analysis of longitudinal data, Springer Verlag, New York
Müller, H.G. 1992: Smooth optimum kernel estimators near endpoints, Biometrika. 78(3), 521–530
Park, B.U.; Marron, J.S. 1991: Comparison of data-driven bandwidth selectors, Journal of the American Statistical Association 85, 66–72
Rajagopalan, B.; Lall, U. 1995: A kernel estimator for discrete distributions, J. Nonparametric Statist. 4, 409–426
Schuster, E. 1985: Incorporating support constraints into nonparametric estimators of densities, Communication in Statistics A14, 1123–1136
Scott, D.W. 1992: Multivariate density estimation: Theory, Practice and Visualization, Wiley series in probability and mathematical statistics, John Wiley and Sons, New York
Scott, D.W.; Tapia, R.A.; Thompson, J.R. 1977: Kernel density estimation revisited, Nonlinear Analysis 1, 339–372
Scott, D.W.; Factor, L.E. 1981: Monte carlo study of three data-based nonparametric density estimators, J. Amer. Statist. Assoc. 76, 9–15
Sheather, S.J. 1983: A data-based algorithm for choosing the window width when estimating the density at a point, Comput. Statist. Data Anal. 1, 229–238
Sheather, S.J. 1986: An improved data-based algorithm for choosing the widnow width when estimating the density at a point, Comput. Statist. Data Anal. 4, 61–65
Sheather, S.J.; Jones, M.C. 1991: A reliable data-based bandwidth selection method for kernel density estimation, J. Royal Statist. Soc. B53, 683–690
Silverman, B.W. 1986: Density estimation for statistics and data analysis, Chapman and Hall, New York
Simonoff, J. 1983: A penalty function approach to smoothing large sparse contingency tables, Annals of Statist. 11, 208–218
Wang, M.C.; Van Ryzin, J. 1981: A Class of smooth estimators for discrete distributions, Biometrika 68(1), 301–309
Woodroofe, M. 1970: On choosing a delta-sequence, Annal. Math. Statist. 41, 1665–1671
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Rajagopalan, B., Lall, U. & Tarboton, D.G. Evaluation of kernel density estimation methods for daily precipitation resampling. Stochastic Hydrol Hydraul 11, 523–547 (1997). https://doi.org/10.1007/BF02428432
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DOI: https://doi.org/10.1007/BF02428432