Skip to main content

D-Optimal Designs for Regression Models with Length-Biased Poisson Response

  • Conference paper
mODa 8 - Advances in Model-Oriented Design and Analysis

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

  • 807 Accesses

Abstract

This paper is concerned with the search for locally optimal designs when the observations of the response variable arise from a weighted distribution in an exponential family. The expression for the information matrices for length-biased distributions from an exponential family are obtained. Locally D-optimal designs are derived for regression models whose response variable follows a weighted Poisson distribution. Two link functions are considered for these models.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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.

References

  • Burridge J, Sebastiani P (1992) Optimal designs for generalized linear models. J Ital Statist Soc 2:183–202

    Article  Google Scholar 

  • Chernoff H (1953) Locally optimal designs for estimating parameters. Ann Math Statist 24:586–602

    MathSciNet  Google Scholar 

  • Feller W (1971) An Introduction to Probability Theory and its Applications. John Wiley & Sons, New York

    MATH  Google Scholar 

  • Fisher R (1934) The effect of methods of ascertainment upon the estimation of frequencies. Annals of Eugenics 6:13–25

    Google Scholar 

  • Ford I, Torsney B, Wu C (1992) The use of a canonical form in the construction of locally optimal designs for non-linear problems. J Roy Statist Soc Ser B 54:569–583

    MATH  MathSciNet  Google Scholar 

  • Nanda A, Jain K (1999) Some weighted distributions results on univariate and bivariate cases. J Statist Plann Inference 77:169–180

    Article  MATH  MathSciNet  Google Scholar 

  • Navarro J, del Águila Y, Ruiz J (2001) Characterizations through reliability measures from weighted distributions. Statist Papers 42:395–402

    Article  MATH  MathSciNet  Google Scholar 

  • Patil G (1981) Studies in statistical ecology involving weighted distributions. Indian Statistical Institute Jubilee International Conference on Statistics: Applications and New Directions 1:478–503

    Google Scholar 

  • Rao C (1965) On discrete distributions arising out of methods of ascertainment. Sankhyā Series A 27:311–324

    MATH  Google Scholar 

  • Rohatgi V (1988) An Introduction to Probability Theory and Mathematical Statistics. John Wiley & Sons, New York

    Google Scholar 

  • Satten G, Kong F, Wright D, Glynn S, Schreiber G (2004) How special is a special interval: modeling departure from length-biased sampling in renewal processes. Biostatistics 5:145–151

    Article  MATH  Google Scholar 

  • Silvey S (1980) Optimum design. Chapman and Hall, London

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Physica-Verlag Heidelberg

About this paper

Cite this paper

Ortiz, I., Rodríguez, C., Martínez, I. (2007). D-Optimal Designs for Regression Models with Length-Biased Poisson Response. In: López-Fidalgo, J., Rodríguez-Díaz, J.M., Torsney, B. (eds) mODa 8 - Advances in Model-Oriented Design and Analysis. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-1952-6_18

Download citation

Publish with us

Policies and ethics