Comparison of Hyperbolic and Constant Width Simultaneous Confidence Bands in Multiple Linear Regression under MVCS...

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Simultaneous confidence bands are crucial for estimating unknown regression models.
• Optimality criteria, like minimum area confidence sets (MACS), are used to compare different confidence bands.
• The minimum volume confidence set (MVCS) criterion generalizes MACS for multiple linear regression.

Purpose of the Study:

• To compare hyperbolic and constant width confidence bands for multiple linear regression models.
• To evaluate these bands under the MVCS criterion within a specific ellipsoidal predictor variable region.
• To determine the conditions under which each band type performs better.

Main Methods:

• Utilizing the minimum volume confidence set (MVCS) criterion for comparison.
• Analyzing confidence bands over a defined ellipsoidal region of predictor variables.
• Investigating the impact of an angle parameter that defines the predictor variable region's size.

Main Results:

• The performance comparison between hyperbolic and constant width confidence bands is dependent on a specific angle.
• For small angles (smaller predictor regions), constant width bands offer a marginal improvement.
• For large angles (larger predictor regions), hyperbolic bands demonstrate substantially better performance.

Conclusions:

• The choice between hyperbolic and constant width confidence bands is context-dependent.
• The size of the predictor variable region, determined by a specific angle, dictates the optimal band choice.
• Hyperbolic bands are more advantageous in scenarios with larger predictor variable regions.