Skip to main content

Nonparametric curve estimation

Some introductory remarks

  • 1317 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 757)

Keywords

  • Spline Function
  • Kernel Estimate
  • Growth Spurt
  • Human Biology
  • Adolescent Growth Spurt

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bartlett, M.S. (1963): Statistical estimation of density functions. Sankhya Sec. A 25 245–254

    MathSciNet  MATH  Google Scholar 

  • Boneva, L.I., Kendall, D.G., and Stefanov, I. (1971): Spline transformations, J. Roy. Statist. Soc. B. 33, 1–70

    MathSciNet  MATH  Google Scholar 

  • Bickel, P.J. and Rosenblatt (1973): On some global measures of the deviations of density function estimates. Ann. Statist. 1, 1071–95

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Bock, R.D., Wainer, H., Petersen, A., Thissen, D., Murray, J., Roche, A. (1973): A parametrization for individual human growth curves, Human Biology 45, 63–80

    Google Scholar 

  • Censov, N.N. (1962): Evaluation of an unknown distribution density from observations. Soviet Math. 3, 1559–1562

    Google Scholar 

  • Clark, R.M. (1974): A survey of statistical problems in archaeological dating. J. Multiv. Anal. 4, 308–326

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Kendall, D.G. (1974): Hunting quanta. Phil. Trans. Roy. Soc. London, A 276, 231–266

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Komlos, J., Major, P. and Tusnady, G. (1975): An approximation of partial sums of independent random variables. Zeit. für Wahr. 32, 111–131

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Largo, R.H., Stützle, W., Gasser, T., Huber, P.J., Prader, A. (1978): A description of the adolescent growth spurt using smoothing spline functions. Annals of Human Biology, in print.

    Google Scholar 

  • Lawton, W.H., Sylvestre, E.A., Maggio, M.S. (1972): Self modeling nonlinear regression. Technometrics 14, 513–532

    CrossRef  MATH  Google Scholar 

  • Lii, K.S., Rosenblatt, M. (1975): Asymptotic behavior of a spline estimate of a density function. Comput. Math. Appl. 1, 223–235

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Mack, Y.P. and Rosenblatt, M. (1979): Multivariate k-nearest neighbor density estimates. J. Multiv. Anal. 9, 1–15

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Marubini, E., Resele, L.F., Barghini, G. (1971): A comparative fitting of gompertz and logistic functions to longitudinal height data during adolescense in girls. Human Biology 43, 237–252

    Google Scholar 

  • Parzen, E. (1962): On the estimation of a probability density and mode. Ann. Math. Statist. 33, 1065–1076

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Preece, M.A., Baines, M.J. (1978): A new family of mathematical models describing the human growth curve. Annals of Human Biology, 5, 1–24

    CrossRef  Google Scholar 

  • Reinsch, Ch. (1967): Smoothing by spline functions. Num. Math. 10, 177–183

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Rosenblatt, M. (1956): Remarks on some nonparametric estimates of a density function. Ann. Math. Statist. 27, 832–837

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Rosenblatt, M. (1970): Density estimates and Markov sequences. In Nonparametric Techniques in Statistical Inference, M. Puri ed. 199–210

    Google Scholar 

  • Rosenblatt, M. (1971): Curve estimates. Ann. Math. Statist. 42, 1815–1842

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Silverman, B.W. (1978): Choosing a window width when estimating a density. Biometrika 65, 1–11

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Silverman, B.W. (1979): Density estimation: are theoretical results useful in practice?-presented at a meeting in honor of W. Hoeffding

    Google Scholar 

  • Stützle, W. (1977): Estimation and parametrization of growth curves. Thesis 6039 ETH Zürich

    Google Scholar 

  • Stützle, W., Gasser, Th., Largo, R., Huber, P.J., Prader, A., Molinari, L. (1979): Shape-invariant modeling of human growth. Mimeographed manuscript, 1979

    Google Scholar 

  • Tanner, J.M., Whitehouse, R.H., Takaishi, M. (1966): Standards from birth to maturity for height, weight, height velocity and weight velocity: British Children. Archives of Disease in Childhood 41, 451–471, 613–635

    Google Scholar 

  • Tarter, M. and Raman, S. (1972): A systematic approach to graphical methods in biometry. Proceedings of 6th Berkeley Symposium vol. IV, 199–222

    MathSciNet  Google Scholar 

  • Van Ness, J.W. and Simpson, C. (1976): On the effects of dimension in discriminant analysis. Technometrics 18, 175–187

    CrossRef  MATH  Google Scholar 

  • Wahba, G., Wold, S. (1975): A completely automatic French curve: Fitting spline functions by cross-validation. Communications in statistics 4, 1–17

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1979 Springer-Verlag

About this paper

Cite this paper

Gasser, T., Rosenblatt, M. (1979). Nonparametric curve estimation. In: Gasser, T., Rosenblatt, M. (eds) Smoothing Techniques for Curve Estimation. Lecture Notes in Mathematics, vol 757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098487

Download citation

  • DOI: https://doi.org/10.1007/BFb0098487

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09706-8

  • Online ISBN: 978-3-540-38475-5

  • eBook Packages: Springer Book Archive