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Consistent directions for least‐squares estimates
Author(s) -
Massam Hélène
Publication year - 1987
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314865
Subject(s) - consistency (knowledge bases) , least squares function approximation , mathematics , set (abstract data type) , combinatorics , statistics , geometry , computer science , estimator , programming language
The least‐squares estimate θ n = X n + y n of the parameter θ in the linear model Y n = X n θ + ϵ n may not be consistent, but there may be directions u such that u 'θ n tends to u 'θ in some sense. This set of directions u has been characterized in two different papers: Drygas (1976) and Wu (1980). The conditions for consistency appear to be different in the two papers. The purpose of this note is to show that the two conditions are equivalent and that they both show that the consistent directions depend upon the geometry of the row vectors v i , i = 1,…, n , of X n with respect to the direction u.