Uncertainty Quantification in Dimension Reduction: Application to Stock Market Analysis

Music City Center 

Dimension reduction is vital for high-dimensional data analysis, yet selecting the intrinsic dimension presents significant challenges due to variability across methods and a lack of consensus on criteria. This study introduces novel hypothesis testing with semiparametric and parametric bootstrap-based approaches to quantify the uncertainty associated with determining the intrinsic dimension. We develop efficient algorithms to construct confidence intervals with desirable coverage rates and valid type I error for hypothesis testing. We apply our method to daily stock returns and identify the intrinsic dimension that effectively captures the data structure. Confidence intervals at different alpha levels are constructed to assess uncertainty. This study provides a systematic framework for uncertainty quantification in dimension reduction, with applicability to different dimension reduction techniques.

Uncertainty Quantification

Dimension Reduction

Stock Market Analysis

Principal Component Analysis