Conservative confidence intervals on multiple correlation coefficient for high-dimensional elliptical data using...

Area of Science:

• Statistics
• High-Dimensional Data Analysis
• Biostatistics

Background:

• The multiple correlation coefficient (MCC) measures linear relationships between variables.
• Classical confidence intervals for MCC are not applicable in high-dimensional settings (p >> n).
• Sample covariance matrix singularity prevents traditional MCC interval estimation.

Purpose of the Study:

• To develop usable confidence intervals for the population MCC in high-dimensional elliptical data.
• To address limitations of classical methods in high-dimensional statistics.
• To evaluate the performance of novel confidence intervals.

Main Methods:

• Utilized random projection methodology for interval construction.
• Developed conservative confidence intervals for the population MCC.
• Conducted simulations to assess coverage probability and interval length.
• Validated methods on real gene expression datasets.

Main Results:

• Proposed confidence intervals are effective for high-dimensional elliptical data.
• Simulations demonstrated the performance of the new intervals.
• Experimental validation confirmed applicability on gene expression data.

Conclusions:

• The random projection method provides a viable alternative for MCC confidence intervals in high-dimensional scenarios.
• The developed intervals offer a practical solution where classical methods are unusable.
• This research contributes to statistical analysis of high-dimensional biological data.