Asymptotic comparison of a class of nonparametric tests with the

ASYMPTOTIC COMPARISON OF A CLASS OF NONPARAMETRIC TESTS WITH THE STUDENT TEST UDC 519.21

Yd. Yu. Nikitin

For the group of integral tests of homogeneity,

generalizing the omega-square

tests, one finds a lower bound of the Pitman asymptotic relative efficiency relative to the Student test for the shift alternative.

X4,X~,...,X~

Let functions

F~

tinuous w i t h a

,~2 ..... ~

and ~

and

F(~-e)

be two independent samples with general distribution

respectively.

bounded density

~

We assume that function

and finite variance

~E>O

.

F

is absolutely con-

We introduce the following

notations:

F.~ and

are the empirical distribution functions,

G~

the second sample

respectively,

and

~=~

~§

constructed from

H-~" ~ # 0

first

and

0-:~