# On Tests for Detecting Change in the Multivariate Mean

• M. S. Srivastava
Chapter
Part of the NATO Advanced study Institutes Series book 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.

## Key Words

detecting a change point multivariate mean likelihood ratio test and estimate distribution of test statistics

## References

1. Bhattacharya, G.K., Johnson, R.A. (1968). Nonparametric tests for shift at an unknown point Annals of Mathematical Statistics, 39, 1731–1743.
2. 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.
3. Gardner, L.A. (1969). On detecting changes in the mean of normal variables Annals of Mathemtical Statistics, 40, 116–126.
4. Illinois Department of Transportation. (1972). Illinois Motor Vehicle Accident Facts, Springfield, Illinois.Google Scholar
5. Page, E.S. (1955). A test for a change in parameter occurring at an unknown point. Biometrika, 42, 523–526.
6. Sen, A.K. (1971). Tests for change in mean and a sequential ranking procedure. Ph.D. thesis, University of Toronto.Google Scholar
7. Sen, A.K., Srivastava, M.S. (1973). On multivariate tests for detecting change in mean. Sankhyā, A, 35, 173–185.
8. Sen, A.K., Srivastava, M.S. (1975a). On tests for detecting change in mean. Annals of Statistics, 3, 98–108.
9. 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
10. Sen, A.K., Srivastava, M.S. (1975c). Some one-sided tests for change in level. Technometrics, 17, 61–64.
11. Srivastava, M.S., Khatri, C.G. (1979). An Introduction to Multivariate Statistics, North Holland Publishing Co., New York.