A Randomized Sequential Procedure to Determine the Number of Factors Article Swipe

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Mathematics Eigenvalues and eigenvectors Test statistic Covariance matrix Statistic Statistics Bounded function Applied mathematics Statistical hypothesis testing Test (biology) Matrix (chemical analysis) Sequential analysis Block (permutation group theory) Null hypothesis Algorithm Combinatorics Mathematical analysis Materials science Biology Composite material Quantum mechanics Paleontology Physics

Lorenzo Trapani ·

YOU? · · 2017 · Open Access · · DOI: https://doi.org/10.1080/01621459.2017.1328359 · OA: W2633758049

This article proposes a procedure to estimate the number of common factors k in a static approximate factor model. The building block of the analysis is the fact that the first k eigenvalues of the covariance matrix of the data diverge, while the others stay bounded. On the grounds of this, we propose a test for the null that the ith eigenvalue diverges, using a randomized test statistic based directly on the estimated eigenvalue. The test only requires minimal assumptions on the data, and no assumptions are required on factors, loadings or idiosyncratic errors. The randomized tests are then employed in a sequential procedure to determine k. Supplementary materials for this article are available online.