Estimation in regression models with externally estimated parameters

Area of Science:

• Statistics
• Mathematical Modeling

Background:

• Regression models often use parameters estimated from separate data sources.
• This approach is common in compartment modeling with external input functions.

Purpose of the Study:

• To develop and present methods for calculating standard errors that account for all sources of variability.
• To improve the accuracy of parameter estimation in regression models using external data.

Main Methods:

• Asymptotic approaches for standard error calculation.
• Bootstrap-based methods for assessing variability.
• Integration of estimates from separate data sources into primary regression models.

Main Results:

• The proposed methods provide accurate standard errors for estimated regression parameters.
• Simulations demonstrate the effectiveness of the asymptotic and bootstrap approaches.
• Examples illustrate the practical application of these techniques.

Conclusions:

• The presented methods effectively address the challenge of multi-source data in regression.
• Accurate standard error computation is crucial for reliable parameter estimation in complex models.