Approximate factor models with weaker loadings. (English) Zbl 07704519
Summary: Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where \(\boldsymbol{\Lambda}^{0'}\boldsymbol{\Lambda}^0/N^\alpha\) is positive definite in the limit when \(\alpha=1\), early work established convergence of the principal component estimates of the factors and loadings up to a rotation matrix. This paper shows that the estimates are still consistent and asymptotically normal when \(\alpha\in(0,1]\) albeit at slower rates and under additional assumptions on the sample size. The results hold whether \(\alpha\) is constant or varies across factor loadings. The framework developed for heterogeneous loadings and the simplified proofs that can be also used in strong factor analysis are of independent interest.
MSC:
| 62-XX | Statistics |
| 91-XX | Game theory, economics, finance, and other social and behavioral sciences |
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