TY - JOUR

T1 - Hodges-Lehmann and Chernoff efficiencies of linear rank statistics

AU - Nikitin, Ya Yu

PY - 1991/1/1

Y1 - 1991/1/1

N2 - Linear rank statistics for the two-sample problem are considered. Under general conditions on the score function and the distribution of the observations large deviation asymptotics for these statistics under the alternative are obtained. After using the Sanov principle an external problem of minimization of the Kullback-Leibler information is solved by means of the calculus of variations and nonlinear analysis. As an application Hodges-Lehmann and Chernoff efficiencies are evaluated. It is shown that they coincide locally with the Pitman, Bahadur and intermediate efficiencies.

AB - Linear rank statistics for the two-sample problem are considered. Under general conditions on the score function and the distribution of the observations large deviation asymptotics for these statistics under the alternative are obtained. After using the Sanov principle an external problem of minimization of the Kullback-Leibler information is solved by means of the calculus of variations and nonlinear analysis. As an application Hodges-Lehmann and Chernoff efficiencies are evaluated. It is shown that they coincide locally with the Pitman, Bahadur and intermediate efficiencies.

KW - Bahadur efficiency

KW - Chernoff efficiency

KW - comparison density

KW - empirical measure

KW - Hodges-Lehmann efficiency

KW - implicit operator

KW - Kullback-Leibler information

KW - large deviations

KW - Linear rank statistics

UR - http://www.scopus.com/inward/record.url?scp=44949277614&partnerID=8YFLogxK

U2 - 10.1016/0378-3758(91)90006-Z

DO - 10.1016/0378-3758(91)90006-Z

M3 - Article

AN - SCOPUS:44949277614

VL - 29

SP - 309

EP - 323

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 3

ER -