SOME SIMPLE TEST PROCEDURES FOR NORMAL MEAN VECTOR WITH INCOMPLETE DATA

K. KRISHNAMOORTHY AND MARUTHY K. PANNALA

Department of Statistics, University of Southwestern Louisiana, Lafayette, LA 70504-1006, U.S.A.

(Received December 25, 1996; revised October 20, 1997)

Abstract. The problem of testing normal mean vector when the observations are missing from subsets of components is considered. For a data matrix with a monotone pattern, three simple exact tests are proposed as alternatives to the traditional likelihood ratio test. Numerical power comparisons between the proposed tests and the likelihood ratio test suggest that one of the proposed tests is indeed comparable to the likelihood ratio test and the other two tests perform better than the likelihood ratio test over a part of the parameter space. The results are extended to a nonmonotone pattern and illustrated using an example.

Key words and phrases: Fisher’s method of combining independent tests, likelihood ratio test, missing data, monotone pattern, power, Tippett’s test, unionintersection test.