On a class of rank scores tests for censored data

Summary

It is well known that one-sample orc-sample (location) problems are special cases of the general linear regression modelY _i =β₁ x _1i +⋯+β _k x _ki +ε _i , where we wish to test the hypothesisH:β₁=⋯=β _q =0,q⪳. This problem has been considered by Hájek [5] and Srivastava [13], [14], and a class of asymptotically most powerful rank score tests has been proposed. In this paper, the above problem of testingH against a sequence of alternatives tending toH at a suitable rate has been considered for thecensored data, i.e., when only the firstr-ordered observations are available. A class of rank score tests has been proposed. It has been shown that the proposed test is superior to those proposed by Gastwirth [6], Sobel [10], [11] and Basu [1], [2], [3], in the sense defined in Section 4; no large sample comparison with Rao, Savage and Sobel [8] statistic is possible since its asymptotic distribution is not known.

Thec-sample problem as a special case of the regression model has been considered in Section 3. In this case, however, the design matrixX _r , becomes a random variable.