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ON TESTS OF SYMMETRY FOR DISCRETE POPULATIONS
Author(s) -
Shirahata Shingo
Publication year - 1974
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1974.tb00919.x
Subject(s) - mathematics , rank (graph theory) , rounding , symmetry (geometry) , null hypothesis , statistical hypothesis testing , statistics , asymptotic distribution , local asymptotic normality
Summary In this paper problems of tests of symmetry about the origin with discrete samples are considered. Recently Vorličková established the asymptotic normality of linear rank statistics and signed rank statistics in [5] and [6]. Here we propose statistics which are conditionally the sum of independent variables, including the locally most powerful tests for a one sided one parameter family. Their asymptotic distributions are derived under the null hypothesis and the contiguous rounding off location alternatives. We propose four types of signed rank tests and investigate their properties.