Optimal design of experiments for functional linear models with dynamic factors

Area of Science:

• Statistics
• Experimental Design
• Functional Data Analysis

Background:

• Linear regression models are widely used for analyzing relationships between variables.
• Estimating functional coefficients precisely is crucial for understanding complex dynamic systems.
• Existing optimal design methods may not fully address continuous functional responses and factors.

Purpose of the Study:

• To develop optimal experimental designs for precise estimation of functional coefficients in linear regression models.
• To extend classical optimal design definitions to functional coefficient estimators.
• To illustrate the methodology with a pharmaceutical manufacturing example.

Main Methods:

• Derivation of the variance-covariance matrix for the functional coefficient estimator.
• Minimization of the integrated sum of square of errors.
• Formulation of A-optimal and D-optimal design expressions for functional coefficients.
• Computation of optimal designs for dynamic experimental factors using algorithms.

Main Results:

• The study provides explicit expressions for A-optimal and D-optimal designs.
• Optimal designs were computed for dynamic experimental factors under various basis function scenarios.
• The methodology was validated through a practical application in pharmaceutical manufacturing.

Conclusions:

• The proposed optimal experimental designs enable precise estimation of functional coefficients.
• The methodology is feasible and offers advantages for real-world applications, particularly in process optimization.
• This work contributes to the advancement of optimal design theory for functional data.