Skip to main content

Part of the book series: Springer Series in Statistics ((SSS))

  • 789 Accesses

Abstract

1The class of all possible consistent estimates of a given parameter c is very extensive and it includes a number of particular practically important estimates thoroughly studied in many statistical texts (see, e.g., Cramér, 1946; Wilks, 1962; Kendall and Stuart, 1966; Silvey, 1970; Zacks, 1971). To compare two different unbiased consistent estimators of c, say, C *N and C **N , the relative efficiency er(C **N , C *N ) or C **N as compared with C *N is sometimes evaluated by the formula er(C **N ,C *N ) = σ2(C *N )/σ2(C **N ). Clearly, C **N is preferable to C *N if, and only if, er(C **N C *N ) > 1. Note also that under some general conditions the lower bound σ 2N (c) to the variance σ2(C *N ) of any unbiased estimator C *N of a parameter c can be determined, and hence the absolute efficiency e(C *N ) = σ2(C *N )/σ *N (c) of C *N can be evaluated. The estimator C *N (and the estimate c *N ) is called efficient if e(C *N ) = 1 and asymptotically efficient if e(C *N ) → 1 as N → ∞.

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

eBook
USD 9.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Yaglom, A.M. (1987). Chapter 3. In: Correlation Theory of Stationary and Related Random Functions. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4628-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4628-2_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-9090-2

  • Online ISBN: 978-1-4612-4628-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics