A penalization method to estimate the intrinsic dimensionality of data

Liliana Forzani (), Daniela Rodriguez () and Mariela Sued ()
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Liliana Forzani: Universidad Nacional del Litoral
Daniela Rodriguez: Universidad Torcuato Di Tella
Mariela Sued: Universidad San Andrés

Statistical Papers, 2025, vol. 66, issue 2, No 16, 20 pages

Abstract: Abstract We propose a novel penalization method for estimating the intrinsic dimensionality of data within a Probabilistic Principal Components Model, extending beyond the Gaussian case. Unlike existing approaches, our method is designed to handle non-normal data, providing a flexible alternative to traditional factor models. Our procedure identifies the dimension at which the eigenvalues of a scatter matrix stabilize. We establish the consistency of the procedure under mild conditions and demonstrate its robustness across a range of data distributions. A comparative analysis highlights its advantages over existing techniques, making it a valuable tool for dimensionality estimation without relying on distributional assumptions.

Keywords: Intrinsic dimensionality; Probabilistic principal components analysis; Dimension reduction; Sufficient dimension reduction; Non-parametric estimation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01667-0

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