Skip to main content

Bound for the Variance

  • Chapter
  • First Online:
Book cover Examples in Parametric Inference with R
  • 2910 Accesses

Abstract

The history of the lower bounds on the variance of the estimators is long and has many contributors.

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 EPUB and 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
Hardcover Book
USD 99.99
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

References

  • Bhattacharya A (1946) On some analogues of the amount of information and their use in statistical estimation. Sankhya 8:1–14

    MathSciNet  Google Scholar 

  • Bhattacharya A (1950) Unbiased statistics with minimum variance. Proc R Soc Edinburgh 63–69

    Google Scholar 

  • Blyth CR (1974) Necessary and sufficient condition for inequalities of Cramer-Rao type. Ann Stat 2:464–473

    Article  MathSciNet  MATH  Google Scholar 

  • Blyth CR, Roberts DM (1972) On inequalities of Cramer-Rao type and admissibility proof. In: Proceedings of sixth Berkley symposium on mathematical statistics and probability, vol 1. University of California Press, pp 17–30

    Google Scholar 

  • Chapman DG, Robbins H (1951) Minimum variance estimation without regularity assumptions. Ann Math Stat 22:581–586

    Article  MathSciNet  MATH  Google Scholar 

  • Cramer H (1946) Mathematical methods of statistics. Princeton University Press

    Google Scholar 

  • Frechet M (1943) Sur l’ extension de certaines evaluating statistques au cas de petits echantillons. Rev Inst Int Stat 11:182–205

    Article  MATH  Google Scholar 

  • Jadhav DB (1983) On inequalities of Cramer-Rao type. Unpublished M.Phil, Thesis, University of Pune, Pune

    Google Scholar 

  • Joshi VM (1976) On the attainment of the Cramer-Rao lower bound. Ann Stat 4:998–1002

    Article  MathSciNet  MATH  Google Scholar 

  • Kiefer J (1952) On minimum variance estimators. Ann Math Stat 23:627–628

    Article  MathSciNet  MATH  Google Scholar 

  • Rao CR (1945) Information and accuracy attainable in the estimation of statistical parameters. Bull Calcutta Math Soc 37:81–91

    MathSciNet  MATH  Google Scholar 

  • Rohatagi VK, Saleh EAK (2001) An introduction to probability and statistics. Wiley

    Google Scholar 

  • Wijsman RA (1973) On the attainment of Cramer-Rao bound. Ann Stat 538–542

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ulhas Jayram Dixit .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media Singapore

About this chapter

Cite this chapter

Dixit, U.J. (2016). Bound for the Variance. In: Examples in Parametric Inference with R. Springer, Singapore. https://doi.org/10.1007/978-981-10-0889-4_4

Download citation

Publish with us

Policies and ethics