TY - JOUR
T1 - On estimating the mean in a bivariate normal distribution with equal or unequal variances
AU - Lakshminarayan, Choudur K.
AU - Han, Chien Pai
PY - 1997
Y1 - 1997
N2 - This paper considers the problem of estimating the mean μx of one of the components of the bivariate normal distribution with equal variances or unequal variances. When the mean of the other component μy is equal to μx, it is advantageous to pool the two sample means as an estimator of μx. When the experimenter is uncertain whether μx = μy, a preliminary test of significance is used at level α to test μx = μy. Three estimators of μx are considered, (i) preliminary test estimator (PTE), (ii) weighting function estimator (WFE), and (iii) adaptive preliminary test estimator (APTE). The WFE is defined as the linear combination of the two sample means with the weight obtained by minimizing the mean square error. The APTE is a PTE with the weight adopted from WFE. The biases, mean square errors, and relative efficiencies of all the three estimators are studied.
AB - This paper considers the problem of estimating the mean μx of one of the components of the bivariate normal distribution with equal variances or unequal variances. When the mean of the other component μy is equal to μx, it is advantageous to pool the two sample means as an estimator of μx. When the experimenter is uncertain whether μx = μy, a preliminary test of significance is used at level α to test μx = μy. Three estimators of μx are considered, (i) preliminary test estimator (PTE), (ii) weighting function estimator (WFE), and (iii) adaptive preliminary test estimator (APTE). The WFE is defined as the linear combination of the two sample means with the weight obtained by minimizing the mean square error. The APTE is a PTE with the weight adopted from WFE. The biases, mean square errors, and relative efficiencies of all the three estimators are studied.
KW - Adaptive preliminary test estimator
KW - Bias
KW - Mean square error
KW - Monte Carlo simulation
KW - Optimal weight
KW - Preliminary test estimator
KW - Relative efficiency
KW - Weighting function estimator
UR - http://www.scopus.com/inward/record.url?scp=0040052401&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0040052401&partnerID=8YFLogxK
U2 - 10.1080/00949659708811828
DO - 10.1080/00949659708811828
M3 - Article
AN - SCOPUS:0040052401
SN - 0094-9655
VL - 58
SP - 155
EP - 170
JO - Journal of Statistical Computation and Simulation
JF - Journal of Statistical Computation and Simulation
IS - 2
ER -