Skip to main content

Part of the book series: Understanding Complex Systems ((UCS))

  • 1868 Accesses

Summary

This work provides further contribution to the linear properties in a continuous time linear model. We deal with linear sufficiency and linear completeness properties, together with the linear admissibility property. These concepts were originally introduced and characterized in a discrete time context and subsequently were extended by the authors of the present paper to a continuous time linear model. Our objective is to study in depth these properties showing a general unified context where the classical linear model appears as a particular case.

In memory of Marisa.

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 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
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

  1. Baksalary, J.K., Kala, R.: Linear transformations preserving best linear unbiased estimators in a general Gauss-Markoff model. Ann. Statist. 9, 913–916 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  2. Baksalary, J.K., Markiewicz, A.: Admissible linear estimators in restricted linear models. Linear Alg. Appl. 70, 9–19 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  3. Baksalary, J.K., Markiewicz, A.: Admissible linear estimators in the general Gauss-Markov model. J. Statist. Plann. Infer. 19, 349–359 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  4. Berlinet, A., Thomas-Agnan, C.: RKHS in Probability and Statistics. Kluwer Acad. Pub., Boston (2004)

    Google Scholar 

  5. Del Pino, G.E.: On restricted linear estimation for regression in stochastic processes. Statist. Prob. Lett. 3, 9–13 (1985)

    Article  MATH  Google Scholar 

  6. Drygas, H.: Sufficiency and completeness in the general. Gauss-Markov model Sankhya Ser. A 45, 88–98 (1983)

    MATH  MathSciNet  Google Scholar 

  7. Ibarrola, P., Pérez-Palomares, A.: Linear sufficiency and linear admissibility in a continuous time. Gauss-Markov model J. Multiv. Anal. 87, 315–327 (2003)

    MATH  Google Scholar 

  8. Ibarrola, P., Pérez-Palomares, A.: Linear completeness in a continuous time. Gauss-Markov model Statist. Prob. Lett. 69, 143–149 (2004)

    Article  MATH  Google Scholar 

  9. Ibarrola, P., Pérez-Palomares, A.: A decomposition of a linear model. Statist. Prob. Lett. 4, 101–1024 (2009)

    Google Scholar 

  10. Müller, J.: Sufficiency and completeness in the linear model. J. Multivariate Anal. 21, 312–323 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  11. Rao, C.R.: Estimation of parameters in a linear model. Ann. Statist. 4, 1023–1037 (1976)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ibarrola, P., Pérez-Palomares, A. (2011). Linear Properties in a Continuous Time Linear Model. In: Pardo, L., Balakrishnan, N., Gil, M.Á. (eds) Modern Mathematical Tools and Techniques in Capturing Complexity. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20853-9_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-20853-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20852-2

  • Online ISBN: 978-3-642-20853-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics