Skip to main content

Digitalization of Observations Permits Efficient Estimation in Continuous Models

  • Conference paper
Soft Methodology and Random Information Systems

Part of the book series: Advances in Soft Computing ((AINSC,volume 26))

Abstract

We show that under certain conditions finite digitalization of continuous data permits to estimate the parameter by the maximum likelihood method preserving the minimal asymptotic variance achieved in the model without digitalization.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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.

Similar content being viewed by others

References

  1. Beirlant, J., Györfi, L. and Lugosi, G. (1994). On the asymptoic normality of the L1- and L2-errors in histogram density estimation. The Canadian Journal of Statistics 22, 309–318.

    Article  MATH  Google Scholar 

  2. Fedotov, A., Harremoes, P. and Topste, F. (2003). Refinements of Pinsker’s inequality. Transactions of IEEE on Information Theory 49, 1491–1498.

    Article  MATH  Google Scholar 

  3. Györfi, L. and Vajda, I. (2002). Asymptotic distributions for goodness-of-fit statistics in a sequence of multinomial models. Statistics and Probability Letters 56, 57–67.

    Article  MathSciNet  MATH  Google Scholar 

  4. Hobza, T., Molina, I. and Vajda, I. (2004). On convergence of Fisher informations in continuous models with quantized observations. Test,(in press).

    Google Scholar 

  5. Mayoral, A.M., Morales, D., Morales, J. and Vajda, I. (2003). On efficiency of estimation and testing with data quantized to fixed numbers of cells. Metrika 57, 1–27.

    Article  MathSciNet  Google Scholar 

  6. Menéndez, M.L., Morales, D., Pardo, L. and Vajda, I. (2001). Minimum disparity estimators for discrete and continuous models. Applications of Mathematics 6, 439–466.

    Article  Google Scholar 

  7. Morales, D., Pardo, L. and Vajda, I. (2004). On efficient estimation in continuous models based on finitely quantized observations. (Submitted).

    Google Scholar 

  8. Rao, C.R. (1973). Linear Statistical inference and its applications, 2nd Edition. Wiley, New York.

    Book  MATH  Google Scholar 

  9. Serfling, R.J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.

    Book  MATH  Google Scholar 

  10. Vajda, I. (1973). X°-divergence and generalized Fisher information. In: Transactions of the Sixth Prague conference on Information Theory, Statistical Decision Functions and Random Processes. Academia, Prague, pp. 873–886.

    Google Scholar 

  11. Vajda, I. (2002). On convergence of information contained in quantized observations. Transactions of IEEE on Information Theory 48, 2163–2172.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Morales, D., Pardo, L., Vajda, I. (2004). Digitalization of Observations Permits Efficient Estimation in Continuous Models. In: Soft Methodology and Random Information Systems. Advances in Soft Computing, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44465-7_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-44465-7_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22264-4

  • Online ISBN: 978-3-540-44465-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics