= I, 2, not depending on n such that, as

Remark 5.2. Let assumption (M.l) be satisfied with 811 fulfilling Eq. (2.24) and with F(x; 8) = F(x-8), x E R1, () E 8. Let the score function 1/J(x; ()) = 'lj;(x-8), X E R1' e E 8, where 'lj; is a monotone function such that (iv) function \.F(t) has continuous first derivative in a neighborhood of

(v) (vi)

Then assumptions (M.2)-(M.5) are satisfied with

Partial sums are here formed by the simple linear rank statistics k

where R 1 , .•• , R11 are the ranks corresponding to Y1, ..• , Y11 ; ( a11 ( l), ... , a11 (n)) are scores and

Therankbasedestimatorsareintroducedalongthelineoftheleastsquares typeestimators,particularly,weput

li1R(17)=argmax{(k(n'~k))11 ISk.RI;k=l,...,n-I}(6.2) and

IJ1R(G)=argmax{ISk+GR-2Sk.R-sk-G.RI;k=G+I,...,n-G} (6.3)

Theseestimatorshavesimilarlimitpropertiesastheleastsquarestype estimatorsandM-estimators.