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GROUPING PROBLEMS IN DISTRIBUTION‐FREE REGRESSION 1
Author(s) -
Brown B. M.
Publication year - 1985
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.1985.tb00554.x
Subject(s) - symmetry (geometry) , distribution (mathematics) , mathematics , inference , type (biology) , mathematical optimization , computer science , algorithm , mathematical analysis , geometry , artificial intelligence , ecology , biology
Summary In regression models having symmetric errors, exact distribution‐free inference about individual parameters may be carried out by grouping observations, eliminating unwanted parameters within groups, and applying distribution free techniques for the symmetric location parameter problem. Models whose errors have identical but not symmetric distributions may obtain symmetry by taking differences between pairs of observations. Both grouping and differencing involve potential efficiency loss. The choice of an optimal scheme to minimize efficiency loss is expressible as a multi–assignment type of problem, whose solutions, exact and approximate, are discussed.