Kaiser Criterion in Factor Models  

作　　者：Changhu Wang Jianhua Guo Yanyuan Ma Shurong Zheng 

机构地区：[1]School of Mathematical Sciences,Peking University,Beijing 100871,P.R.China [2]School of Mathematics and Statistics,Beijing Technology and Business University,Beijing 100048,P.R.China [3]Department of Statistics,Pennsylvania State University,University Park,Pennsylvania,USA [4]KLAS and School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2025年第2期547-552,共6页数学学报(英文版)

基　　金：Supported by NSFC (Grant Nos. 11631003, 11690012)。

摘　　要：Despite of the wide use of the factor models, the issue of determining the number of factors has not been resolved in the statistics literature. An ad hoc approach is to set the number of factors to be the number of eigenvalues of the data correlation matrix that are larger than one, and subsequent statistical analysis proceeds assuming the resulting factor number is correct. In this work, we study the relation between the number of such eigenvalues and the number of factors, and provide the if and only if conditions under which the two numbers are equal. We show that the equality only relies on the properties of the loading matrix of the factor model. Guided by the newly discovered condition, we further reveal how the model error affects the estimation of the number of factors.

关 键 词：Factor model Kaiser criterion positive definite 

分 类 号：O17[理学—数学]