caa a22 4500 475826728 CHVBK 20180406123830.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1023/A:1004121503274 doi (NATIONALLICENCE)springer-10.1023/A:1004121503274 Bivariate Sign Tests Based on the Sup, L 1 and L 2 Norms [Elektronische Daten] [Denis Larocque, Serge Tardif, Constance van Eeden] The bivariate location problem is considered. The sup, L 1 and L 2 norms are used to construct bivariate sign tests from the univariate sign statistics computed on the projected observations on all lines passing through the origin. The tests so obtained are affine-invariant and distribution-free under the null hypothesis. The sup-norm gives rise to Hodges' test. A class of tests derived from the L 2-norm, with Blumen's test as a member, is seen to be related to a class proposed by Oja and Nyblom (1989, J. Amer. Statist. Assoc., 84, 249-259). The L 1-norm gives rise to a new test. Its asymptotic null distribution is seen to be the same as that of the L 1-norm of a certain normal process related to the standard Wiener process. An explicit expression of its cumulative distribution function is given. A simulation study will examine the merits of the three approaches. The Institute of Statistical Mathematics, 2000 Location problem nationallicence distribution-free nationallicence affine-invariance nationallicence normal process nationallicence Wiener process nationallicence L 1-norm nationallicence L 2-norm nationallicence Hodges' test nationallicence Blumen's test nationallicence Larocque Denis Départment de Mathématiques et de Statistique, Université de Montréal, Montréal, H3C 3J7, Québec, Canada aut Tardif Serge Départment de Mathématiques et de Statistique, Université de Montréal, Montréal, H3C 3J7, Québec, Canada aut van Eeden Constance Department of Statistics, The University of British Columbia, V6T 1Z2, Vancouver, Canada aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/3(2000-09-01), 488-506 0020-3157 52:3<488 2000 52 10463 https://doi.org/10.1023/A:1004121503274 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004121503274 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Larocque Denis Départment de Mathématiques et de Statistique, Université de Montréal, Montréal, H3C 3J7, Québec, Canada aut NATIONALLICENCE 700 1- Tardif Serge Départment de Mathématiques et de Statistique, Université de Montréal, Montréal, H3C 3J7, Québec, Canada aut NATIONALLICENCE 700 1- van Eeden Constance Department of Statistics, The University of British Columbia, V6T 1Z2, Vancouver, Canada aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/3(2000-09-01), 488-506 0020-3157 52:3<488 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer