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.

scholarly journals On the noncentral distribution of the ratio of the extreme roots of wishart matrix

1981 ◽  
Vol 4 (1) ◽  
pp. 147-154
Author(s):  
V. B. Waikar
Keyword(s):  
Nuclear Physics ◽  
Normal Population ◽  
Wishart Distribution ◽  
Exact Distribution ◽  
Multivariate Normal ◽  
Wishart Matrix ◽  
Zonal Polynomials ◽  
Characteristic Roots ◽  
Multivariate Normal Population ◽  
Mean Vector

The distribution of the ratio of the extreme latent roots of the Wishart matrix is useful in testing the sphericity hypothesis for a multivariate normal population. LetXbe ap×nmatrix whose columns are distributed independently as multivariate normal with zero mean vector and covariance matrix∑. Further, letS=XX′and let11>…>1p>0be the characteristic roots ofS. ThusShas a noncentral Wishart distribution. In this paper, the exact distribution offp=1−1p/11is derived. The density offpis given in terms of zonal polynomials. These results have applications in nuclear physics also.

Sample Size and the Accuracy of Predictions Made from Multiple Regression Equations

1982 ◽  
Vol 7 (2) ◽  
pp. 91-104 ◽  
Author(s):  
Richard Sawyer
Keyword(s):  
Sample Size ◽  
Multiple Regression ◽  
Normal Population ◽  
Absolute Error ◽  
Multiple Regression Equation ◽  
Regression Equations ◽  
Multivariate Normal ◽  
Rules Of Thumb ◽  
Multivariate Normal Population ◽  
The Mean

Some rules of thumb are given for estimating the accuracy of predictions based on a multiple regression equation developed from a random sample of a multivariate normal population. The distribution of the prediction error in this case can be approximated usefully by a normal distribution. Formulas are given for the moments of the distribution and for other parameters such as the mean absolute error (MAE). The approximate inflation in MAE (over its asymptotic value) due to estimating the regression coefficients is a simple function of the base sample size and the number of predictors.

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