Hodges-lehmann estimators in the case of grouped data - I
Titel:
Hodges-lehmann estimators in the case of grouped data - I
Auteur:
Padmanabhan, A. R.
Verschenen in:
Communications in statistics
Paginering:
Jaargang 6 (1977) nr. 4 pagina's 371-380
Jaar:
1977
Inhoud:
Let X' = (X'1,…,X'm) and Y' = (Y'1,…,Y'n) be two independent random samples from absolutely continuous distribution functions F' and G' respectively with G'(U) = F'(u-Δ) for all u. Let Xi and Yj be obtained from X'i and Y'j by rounding off to the nearest integer. Let h(X',Y') be any appropriate two-sample statistic. Let [image omitted] and [image omitted] , where N = m + n be the two-sample Hodges-Lehmann (H-L) estimators derived from h(X',Y') and h(X,Y), respectively. (In defining h(X,Y), ties are handled by the method of averaged scores.) We then have, (i)[image omitted] with probability 1. (ii) Prob[image omitted] as N → ∞. And, if Δ is an integer or zero, the stronger result Prob[image omitted] holds. Thus under the null hypothesis[image omitted] is asymptotically degenerate. The efficiency of [image omitted] relative to the usual parametric estimator, is, in a sense to be defined, the same as in the continuous case. If the measurements are very accurate (i.e. if they are rounded off to two or more decimals) , then the large-sample behaviour of [image omitted] is very nearly the same as [image omitted] . A more precise statement is given in Section 6.
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