Skip to main content

Density quantile estimation approach to statistical data modelling

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

Abstract

This paper describes the density-quantile function approach to statistical analysis of a sample as involving five phases requiring the study of various population raw and smoothed quantile and density-quantile functions. The phases can be succinctly described in terms of the notation for the functions studied: (1) Q, fQ, q, (ii) \(\tilde Q,\tilde q\), (iii) \(\tilde fQ\), (iv) \(\hat fQ,\hat d\), d(u)=f0Q0(u)q(u)/σ0, σ0 = ∫ 10 f0Q0(u)q(u)du, (v) \(\hat Q = \hat \mu + \hat \sigma Q_0\).

Research supported by grant DAAG29-78-G-0180 from the Army Research Office.

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

  • Bofinger, E. (1975), "Estimation of a density function using order statistics," Austral. J. Statistics 17, 1–7.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Bofinger, E. (1975), "Non-parametric estimation of density for regularly varying distributions," Austral. J. Statistics 17, 192–195.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Czorgo, M. and Revesz, P. (1978), "Strong Approximations of the Quantile Process," Annals Statistics 6, 882–897.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Parzen, E. (1979), "Non-parametric Statistical Data Modeling," Journal American Statistical Association, 74, 105–131 (with discussion).

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Parzen, E. (1979a), "A Density-quantile function perspective on robust estimation." Robustness in Statistics. ed. R. Launer and G. Wilkinson, New York: Academic Press.

    Google Scholar 

  • Scheffé, H. and Tukey, J. W. (1945), "Non-parametric estimation, I Validation of order statistics," Ann. Math. Statist. 16, 187–192.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Tukey, J. N. (1965), "Which part of the sample contains the information," Proc. Nat. Acad. Sci. 53, 127–134.

    CrossRef  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

Parzen, E. (1979). Density quantile estimation approach to statistical data modelling. 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/BFb0098495

Download citation

  • DOI: https://doi.org/10.1007/BFb0098495

  • 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