A simultaneous testing of the mean vector and the covariance matrix among two populations for high-dimensional data

Test ◽  
2017 ◽  
Vol 27 (3) ◽  
pp. 680-699 ◽  
Author(s):  
Masashi Hyodo ◽  
Takahiro Nishiyama
Keyword(s):  
Covariance Matrix ◽  
High Dimensional Data ◽  
High Dimensional ◽  
Simultaneous Testing ◽  
The Mean ◽  
Mean Vector ◽  
Two Populations

Simultaneous testing of mean vector and covariance matrix for high-dimensional data

2017 ◽  
Vol 188 ◽  
pp. 82-93 ◽  
Author(s):  
Zhongying Liu ◽  
Baisen Liu ◽  
Shurong Zheng ◽  
Ning-Zhong Shi
Keyword(s):  
Covariance Matrix ◽  
High Dimensional Data ◽  
High Dimensional ◽  
Simultaneous Testing ◽  
Mean Vector

scholarly journals Monitoring the mean vector and the covariance matrix of multivariate processes with sample means and sample ranges

Production ◽  
2011 ◽  
Vol 21 (2) ◽  
pp. 197-208 ◽  
Author(s):  
Antônio Fernando Branco Costa ◽  
Marcela Aparecida Guerreiro Machado
Keyword(s):  
Covariance Matrix ◽  
Sample Sizes ◽  
Process Mean ◽  
Multivariate Processes ◽  
Multivariate Case ◽  
The Mean ◽  
Sample Variances ◽  
Mean Vector

The joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and R charts and the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and S² charts are the most common charts used for monitoring the process mean and dispersion. With the usual sample sizes of 4 and 5, the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and R charts are slightly inferior to the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and S² charts in terms of efficiency in detecting process shifts. In this article, we show that for the multivariate case, the charts based on the standardized sample means and sample ranges (MRMAX chart) or on the standardized sample means and sample variances (MVMAX chart) are similar in terms of efficiency in detecting shifts in the mean vector and/or in the covariance matrix. User's familiarity with the computation of sample ranges is a point in favor of the MRMAX chart. An example is presented to illustrate the application of the proposed chart.

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