The Annals of Mathematical Statistics

Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives

Jaroslav Hajek

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Abstract

Results of Chernoff-Savage (1958) and Govindarajulu-LeCam-Raghavachari (1966) are extended from the two-sample case to the general regression case and, simultaneously, the conditions on the scores-generating function are relaxed. The main results are stated in Section 2 and their proofs are given in Section 5. Sections 3 and 4 contain auxiliary propositions, on which the methods of the present paper are based. Section 6 includes a counterexample, showing that the theorem cannot be extended to discontinuous scores-generating functions.

Article information

Source
Ann. Math. Statist., Volume 39, Number 2 (1968), 325-346.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177698394

Digital Object Identifier
doi:10.1214/aoms/1177698394

Mathematical Reviews number (MathSciNet)
MR222988

Zentralblatt MATH identifier
0187.16401

JSTOR
links.jstor.org

Citation

Hajek, Jaroslav. Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives. Ann. Math. Statist. 39 (1968), no. 2, 325--346. doi:10.1214/aoms/1177698394. https://projecteuclid.org/euclid.aoms/1177698394


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