TY - JOUR

T1 - Comparing Two Population Means and Variances

T2 - A Parametric Robust Way

AU - Tsou, Tsung Shan

N1 - Funding Information:
This work is partially supported by NSC grant 38108F of National Science Council, R.O.C.

PY - 2003/10

Y1 - 2003/10

N2 - This article introduces a parametric robust way of comparing two population means and two population variances. With large samples the comparison of two means, under model misspecification, is lesser a problem, for, the validity of inference is protected by the central limit theorem. However, the assumption of normality is generally required, so that the inference for the ratio of two variances can be carried out by the familiar F statistic. A parametric robust approach that is insensitive to the distributional assumption will be proposed here. More specifically, it will be demonstrated that the normal likelihood function can be adjusted for asymptotically valid inferences for all underlying distributions with finite fourth moments. The normal likelihood function, on the other hand, is itself robust for the comparison of two means so that no adjustment is needed.

AB - This article introduces a parametric robust way of comparing two population means and two population variances. With large samples the comparison of two means, under model misspecification, is lesser a problem, for, the validity of inference is protected by the central limit theorem. However, the assumption of normality is generally required, so that the inference for the ratio of two variances can be carried out by the familiar F statistic. A parametric robust approach that is insensitive to the distributional assumption will be proposed here. More specifically, it will be demonstrated that the normal likelihood function can be adjusted for asymptotically valid inferences for all underlying distributions with finite fourth moments. The normal likelihood function, on the other hand, is itself robust for the comparison of two means so that no adjustment is needed.

KW - F test

KW - Likelihood ratio test

KW - Robust profile likelihood

UR - http://www.scopus.com/inward/record.url?scp=0141493722&partnerID=8YFLogxK

U2 - 10.1081/STA-120023263

DO - 10.1081/STA-120023263

M3 - 期刊論文

AN - SCOPUS:0141493722

VL - 32

SP - 2013

EP - 2029

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 10

ER -