Skip to main content

Diskrimination und Klassifikation von Verlaufskurven

  • Conference paper
Neuere Verfahren der nichtparametrischen Statistik

Part of the book series: Medizinische Informatik und Statistik ((MEDINFO,volume 60))

Zusammenfassung

Für viele Fragestellungen der statistischen Praxis sind Verlaufskurven das einfachste Objekt der Beobachtung. Wir verstehen darunter das folgende Modell

$$ {\text{Y(t) = f(t) + Z(t) a}} \leqslant {\text{t}} \leqslant {\text{b}} $$
(1.1)

Dabei ist Y(t) der Prozeß, der zu bestimmten Zeitpunkten t1…,tn beobachtet wird, f(t) ist eine unbekannte Regressionsfunktion, die den Verlauf des interessierenden Phänomens beschreibt und Z(t) ist ein stochastischer Störprozeß, dessen Mittelwertsfunktion E(Z(t)) konstant O ist.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  • Agarwal, G. G. und Studden, W. J. (1980) Asymptotic Integrated Mean Square Error Using Least Squares and Bias Minimizing Splines. Ann. Statist. 8, 1307–1325.

    Article  MathSciNet  MATH  Google Scholar 

  • Azen, S. P. und Afifi, A. A. (1972) Asymptotic and Small Sample Behavior of Estimated Bayes Rules for Classifying Time-Dependent Observations. Biometrics 28, 989–998.

    Article  MathSciNet  Google Scholar 

  • de Boor, C. (1978) A Practical Guide to Splines. Springer, New York.

    Book  MATH  Google Scholar 

  • Borowiak, D. (1983) A Multiple Model Discrimination Procedure. Commun. Statist.-Theor. Meth. 12, 2911–2921.

    Article  MathSciNet  MATH  Google Scholar 

  • Breiman, L., Friedman, J. H., Ohlsen, R. A., Stone, C. J. (1984) Classification and Regression Trees. Wadsworth Int., Belmont, Calif.

    MATH  Google Scholar 

  • Browdy, B. L. und Chang, P. C. (1982) Bayes Procedures for the Classification of Multiple Polynomial Trends With Dependent Residuals. J. Amer. Statist. Ass. 77, 483–487.

    Article  MATH  Google Scholar 

  • Craven, P. und Wahba, C. (1979) Smoothing Noisy Data with Spline Functions. Numer. Math. 31, 377–403.

    Article  MathSciNet  MATH  Google Scholar 

  • Eubank, R. L. (1984) Approximate Regression Models and Splines. Commun. Statist. - Theor. Meth. 13, 433–484.

    Article  MathSciNet  MATH  Google Scholar 

  • Hand, D. J. (1981) Discrimination and Classification. J. Wiley, New York.

    MATH  Google Scholar 

  • Humak, K. M. S. (1983) Statistische Methoden der Modellbildung. Akademieverlag, Berlin.

    MATH  Google Scholar 

  • Kitagawa,G. (1984) State Space Modelling of Nonstationary Time Series and Smoothing of Unequally Spaced Data. In: Time Series Analysis of Irregularly Observed Data, p. 189–209.

    Google Scholar 

  • Springer Lect. Notes Statist. 25.

    Google Scholar 

  • Reinsch, C. H. (1967) Smoothing by Spline Functions. Numer. Math. 10, 177–183.

    Article  MathSciNet  MATH  Google Scholar 

  • Wecker, W. E. und Ansley, C. F. (1983) The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing. J. Amer. Statist. Ass. 78, 81–89.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Grossmann, W. (1985). Diskrimination und Klassifikation von Verlaufskurven. In: Pflug, G.C. (eds) Neuere Verfahren der nichtparametrischen Statistik. Medizinische Informatik und Statistik, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70641-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-70641-7_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15702-1

  • Online ISBN: 978-3-642-70641-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics