Optimal tests for the correlation coefficient in a symmetric multivariate normal population

1986 ◽  
Vol 14 (2-3) ◽  
pp. 263-268 ◽  
Author(s):  
D.V. Gokhale ◽  
Ashis Sen Gupta
Keyword(s):  
Correlation Coefficient ◽  
Normal Population ◽  
Multivariate Normal ◽  
Optimal Tests ◽  
Multivariate Normal Population

Fisher’s Tanh−1 Transformation of the Correlation Coefficient and a Test for Complete Independence in a Multivariate Normal Population

1987 ◽  
Vol 12 (3) ◽  
pp. 294-300
Author(s):  
John R. Reddon
Keyword(s):  
Correlation Coefficient ◽  
Type I Error ◽  
Normal Population ◽  
Error Rates ◽  
Small Samples ◽  
Type I ◽  
Multivariate Normal ◽  
Type I Error Rates ◽  
Complete Independence ◽  
Multivariate Normal Population

Computer sampling from a multivariate normal spherical population was used to evaluate Type I error rates for a test of P = I based on Fisher’s tanh−1 variance stabilizing transformation of the correlation coefficient. The range of variates considered was 5 to 25 and Type I error rates were estimated for several sample sizes with 2,500 independent replications. Except for small samples the test was well behaved. After the test converges to an acceptable Type I error rate it is preferable to Box’s test of P = I.

On Sequential Procedures for the Point Estimation of the Mean Vector

1988 ◽  
Vol 37 (1-2) ◽  
pp. 47-54 ◽  
Author(s):  
R. Karan Singh ◽  
Ajit Chaturvedi
Keyword(s):  
Normal Population ◽  
Stopping Time ◽  
Point Estimation ◽  
Multivariate Normal ◽  
Minimum Risk ◽  
Sequential Procedures ◽  
Multivariate Normal Population ◽  
Bounded Risk ◽  
The Mean ◽  
Mean Vector

Sequential procedures are proposed for (a) the minimum risk point estimation and (b) the bounded risk point estimation of the mean vector of a multivariate normal population . Second-order approximations are derived. For the problem (b), a lower bound for the number of additional observations (after stopping time) is obtained which ensures “ exact” boundedness of the risk associated witb the sequential procedure.

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