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A condition for the regression predictor to be consistent in a single common factor model
Author(s) -
Kano Yutaka
Publication year - 1986
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1986.tb00859.x
Subject(s) - estimator , mathematics , statistics , factor analysis , factor (programming language) , quadratic equation , regression , regression analysis , least squares function approximation , sample (material) , econometrics , computer science , chemistry , geometry , chromatography , programming language
This paper investigates the prediction of a common factor in a single common factor model with infinite items when the structural parameter vector (factor loadings and unique variances) is unknown. A condition in terms of the sample size n and the number of items p is established under which the regression predictor for a unique common factor, in which the parameter vector is replaced by the least squares estimator, converges to it in quadratic mean. The condition is that p → ∞ and p 2 / n → 0 under some mild assumptions.