scholarly journals Estimating the Mean of a Multivariate Normal Population with General Quadratic Loss Function

1966 ◽  
Vol 37 (6) ◽  
pp. 1819-1824 ◽  
Author(s):  
P. K. Bhattacharya
Keyword(s):  
Loss Function ◽  
Normal Population ◽  
Quadratic Loss ◽  
Multivariate Normal ◽  
Quadratic Loss Function ◽  
Multivariate Normal Population ◽  
The Mean

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 Baranchick-type Estimators of a Multivariate Normal Mean Under the General Quadratic Loss Function

2020 ◽  
pp. 608-621
Author(s):  
Abdenour Hamdaoui ◽  
Abdelkader Benkhaled ◽  
Mekki Terbeche
Keyword(s):  
Loss Function ◽  
General Situation ◽  
Quadratic Loss ◽  
Shrinkage Estimators ◽  
Multivariate Normal ◽  
Multivariate Normal Mean ◽  
The Matrix ◽  
Normal Mean ◽  
Stein Estimator ◽  
The Mean

The problem of estimating the mean of a multivariate normal distribution by different types of shrinkage estimators is investigated. We established the minimaxity of Baranchick-type estimators for identity covariance matrix and the matrix associated to the loss function is diagonal. In particular the class of James-Stein estimator is presented. The general situation for both matrices cited above is discussed

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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