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Smoothing Techniques for Visualisation

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Part of the book series: Springer Handbooks Comp.Statistics ((SHCS))

Abstract

Graphical displays are often constructed to place principal focus on the individual observations in a dataset, and this is particularly helpful in identifying both the typical positions of datapoints and unusual or influential cases. However, in many investigations, principal interest lies in identifying the nature of underlying trends and relationships between variables, and so it is often helpful to enhance graphical displays in wayswhich give deeper insight into these features.This can be very beneficial both for small datasets, where variation can obscure underlying patterns, and large datasets, where the volume of data is so large that effective representation inevitably involves suitable summaries.

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References

  • Adler, D. (2005) The R package rgl: 3D visualization device system (OpenGL) Version 0.65, available from cran.r-project.org.

    Google Scholar 

  • Bock, M., Bowman, A.W. and Ismail, B. (2005) Estimation and inference for error variance in bivariate nonparametric regression. Technical report, Department of Statistics, The University of Glasgow.

    Google Scholar 

  • Bowman, A.W. and Azzalini, A. (1997) Applied Smoothing Techniques for Data Analysis. Oxford University Press, Oxford.

    MATH  Google Scholar 

  • Bowman, A.W. and Azzalini, A. (2005) The R package sm: Smoothing methods for nonparametric regression and density estimation. Version 2.1-0, available from cran.r-project.org.

    Google Scholar 

  • Bowman, A. (2005) Comparing nonparametric surfaces. Technical report, Department of Statistics, The University of Glasgow. (Available from www.stats.gla.ac.uk/∼ adrian.

    Google Scholar 

  • Cleveland, W.S. (1993) Visualising Data. Hobart Press, Summit, NJ.

    Google Scholar 

  • Cole, T.J. and Green, P.J. (1992) Smoothing reference centile curves: the LMS method and penalised likelihood. Statistics in Medicine 11:1305–1319.

    Article  Google Scholar 

  • Cook, R.D. and Weisberg, S. (1994). An Introduction to Regression Graphics. Wiley, New York.

    MATH  Google Scholar 

  • Diblasi, A. and Bowman, A.W. (2001) On the use of the variogram for checking independence in a Gaussian spatial process. Biometrics, 57:211–218.

    Article  MathSciNet  Google Scholar 

  • Fan, J. and Gijbels, I. (1996). Local polynomial modelling and its applications. Chapman & Hall, London.

    MATH  Google Scholar 

  • Fan, J., Heckmann, N.E. and Wand, M.P. (1995). Local polynomial kernel regression for generalized linear models and quasi likelihood functions. J. Amer. Statist. Assoc, 90:141–50.

    Article  MATH  MathSciNet  Google Scholar 

  • Friedman, J.H. and Stuetzle, W. (1981) Projection pursuit regression. J. Amer. Statist. Assoc., 76:817–23.

    Article  MathSciNet  Google Scholar 

  • Gasser, T., Sroka, L. and Jennen-Steinmetz, C. (1986) Residual variance and residual pattern in nonlinear regression. Biometrika, 73:625–33.

    Article  MATH  MathSciNet  Google Scholar 

  • Green, P.J. and Silverman, B.W. (1994) Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. Chapman & Hall, London.

    MATH  Google Scholar 

  • Härdle, W., Müller, M., Sperlich, S., Werwatz, A. (2004) Nonparametric and Semiparametric Models. Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • Hastie, T. (2005) The R package gam: Generalized Additive Models, Version 0.94, available from cran.r-project.org.

    Google Scholar 

  • Hastie, T. and Tibshirani, R. (1990) Generalized Additive Models. Chapman & Hall, London.

    MATH  Google Scholar 

  • Horowitz, J.L. (2004) Semiparametric models. In: Gentle, J.E., Härdle, W. and Mori, Y. (eds) Handbook of Computational Statistics: concepts and methods. Springer, Berlin.

    Google Scholar 

  • Hurvich, C.M., Simonoff, J.S. and Tsai, C.-L. (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion, J.Roy.Stat.Soc., Series B, 60:271–293.

    Article  MATH  MathSciNet  Google Scholar 

  • Kim, H.T. and Truong, Y.K. (1998) Nonparametric regression estimates with censored data: local linear smoothers and their applications, Biometrics 54:1434–1444.

    Article  MATH  MathSciNet  Google Scholar 

  • Loader, C. (2004) Smoothing: local regression techniques. In: Gentle, J.E., Härdle, W. and Mori, Y. (eds) Handbook of Computational Statistics: concepts and methods. Springer, Berlin.

    Google Scholar 

  • McMullan, A., Bowman, A.W. and Scott, E.M. (2003). Non-linear and nonparametric modelling of seasonal environmental data. Computational Statistics, 18:167–183.

    MATH  MathSciNet  Google Scholar 

  • McMullan, A., Bowman, A.W. and Scott, E.M. (2005). Additive models with correlated data: an application to the analysis of water quality data. Technical report, Department of Statistics, The University of Glasgow. (Available from www.stats.gla.ac.uk/∼ adrian).

    Google Scholar 

  • Mammen, E., Linton, O.B. and Nielsen, T.J. (1999) The existence and asymptotic properties of a backfitting projection algorithm under weak conditions. Annals of Statistics 27:1443–1490.

    MATH  MathSciNet  Google Scholar 

  • Munk, A., Bissantz, N., Wagner, T. and Freitag, G. (2005) On difference-based variance estimation in nonparametric regression when the covariate is high-dimensional. J. Roy. Statistic. Soc., Series B, 67:19–41.

    Article  MATH  MathSciNet  Google Scholar 

  • Nielsen, T.J. and Sperlich, S. (2005) Smooth backfitting in practice. J. Roy. Statistic. Soc., Series B, 67:43–61.

    Article  MATH  MathSciNet  Google Scholar 

  • Percival, D.B. and Walden, A.T. (2000) Wavelet Methods for Time Series Analysis. Cambridge University Press, Cambridge.

    MATH  Google Scholar 

  • Poiner, I.R., Blaber, S.J.M., Brewer, D.T., Burridge, C.Y., Caesar, D., Connell, M., Dennis, D., Dews, G.D., Ellis, A.N., Farmer, M., Fry, G.J., Glaister, J., Gribble, N., Hill, B.J., Long, B.G., Milton, D.A., Pitcher, C.R., Proh, D., Salini, J.P., Thomas, M.R., Toscas, P., Veronise, S., Wang, Y.G., Wassenberg, T.J. (1997) The effects of prawn trawling in the far northern section of the Great Barrier Reef. Final report to GBRMPA and FRDC on 1991–96 research. CSIRO Division of Marine Research, Queensland Dept. of Primary Industries.

    Google Scholar 

  • R Development Core Team (2004) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org.

    Google Scholar 

  • Ruppert, D., Wand, M.P. and Carroll, R.J. Semiparametric Regression. Cambridge University Press, Cambridge.

    Google Scholar 

  • Schimek, M. (2000) Smoothing and Regression: Approaches, Computation and Application. Wiley, New York.

    MATH  Google Scholar 

  • Simonoff, J.S. (1996) Smoothing Methods in Statistics. Springer-Verlag, New York.

    MATH  Google Scholar 

  • Wood, S.N. (2000) Modelling and smoothing parameter estimation with multiple quadratic penalties. J.Roy.Stat.Soc., Series B, 62:413–428.

    Article  Google Scholar 

  • Wood, S.N. (2005) The R package mgcv: GAMs with GCV smoothness estimation and GAMMs by REML/PQL. Version, 1.3-9 available from cran.r-project.org.

    Google Scholar 

  • Wood, S.N. (2006) Generalized Additive Models: An Introduction with R. CRC Press, London.

    MATH  Google Scholar 

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Bowman, A. (2008). Smoothing Techniques for Visualisation. In: Handbook of Data Visualization. Springer Handbooks Comp.Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-33037-0_20

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