Skip to main content

On Tests for Detecting Change in the Multivariate Mean

  • Chapter

Part of the book series: NATO Advanced study Institutes Series ((ASIC,volume 79))

Summary

We consider tests based on one observation on each of N ≥ 2 random vectors x 1,…,x N to decide if the mean vectors μ of the x i’s are all equal against the alternative that a change has occurred at some unknown point r, (i.e., μ 1 = μ2 =… = μ rμ r+1 =…= μ N). The x i’s are assumed to be normally distributed with common unknown covariance. An estimate of the change point r is also given.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bhattacharya, G.K., Johnson, R.A. (1968). Nonparametric tests for shift at an unknown point Annals of Mathematical Statistics, 39, 1731–1743.

    MathSciNet  Google Scholar 

  • Chernoff, H., Zacks, S. (1964). Estimating the current mean of a normal distribution which is subject to changes in time. Annals of Mathematical Statistics, 35, 990–1018.

    Article  MathSciNet  Google Scholar 

  • Gardner, L.A. (1969). On detecting changes in the mean of normal variables Annals of Mathemtical Statistics, 40, 116–126.

    Article  Google Scholar 

  • Illinois Department of Transportation. (1972). Illinois Motor Vehicle Accident Facts, Springfield, Illinois.

    Google Scholar 

  • Page, E.S. (1955). A test for a change in parameter occurring at an unknown point. Biometrika, 42, 523–526.

    MathSciNet  MATH  Google Scholar 

  • Sen, A.K. (1971). Tests for change in mean and a sequential ranking procedure. Ph.D. thesis, University of Toronto.

    Google Scholar 

  • Sen, A.K., Srivastava, M.S. (1973). On multivariate tests for detecting change in mean. Sankhyā, A, 35, 173–185.

    MathSciNet  MATH  Google Scholar 

  • Sen, A.K., Srivastava, M.S. (1975a). On tests for detecting change in mean. Annals of Statistics, 3, 98–108.

    Article  MathSciNet  MATH  Google Scholar 

  • Sen, A.K., Srivastava, M.S. (1975b). On tests for detecting change in mean when variance is unknown. Annals of the Institute of Statictical Mathematics, 479–486.

    Google Scholar 

  • Sen, A.K., Srivastava, M.S. (1975c). Some one-sided tests for change in level. Technometrics, 17, 61–64.

    Article  MATH  Google Scholar 

  • Srivastava, M.S., Khatri, C.G. (1979). An Introduction to Multivariate Statistics, North Holland Publishing Co., New York.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1981 D. Reidel Publishing Company

About this chapter

Cite this chapter

Srivastava, M.S. (1981). On Tests for Detecting Change in the Multivariate Mean. In: Taillie, C., Patil, G.P., Baldessari, B.A. (eds) Statistical Distributions in Scientific Work. NATO Advanced study Institutes Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8552-0_15

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-8552-0_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-8554-4

  • Online ISBN: 978-94-009-8552-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics