An asymptotic and empirical smoothing parameters selection method for smoothing spline ANOVA models in large samples

Area of Science:

• Statistics
• Computational Statistics
• Data Science

Background:

• Classic statistical models like smoothing spline ANOVA models face computational challenges with large datasets.
• High computational costs, especially in selecting smoothing parameters, limit the practicality of these models for large-scale data analysis.

Purpose of the Study:

• To develop an efficient smoothing parameter selection method for smoothing spline ANOVA models applicable to large samples.
• To overcome the computational burden associated with traditional methods in high-dimensional and large sample scenarios.

Main Methods:

• Developed an "asympirical" (asymptotic and empirical) method for smoothing parameter selection.
• Utilized asymptotic analysis to establish the polynomial relationship between optimal smoothing parameters, sample size, and an unknown constant.
• Estimated the unknown constant via empirical subsample extrapolation.

Main Results:

• The proposed method significantly reduces computational costs for smoothing parameter selection in large samples.
• Demonstrated that the selected smoothing parameters converge to optimal values that minimize a specific risk function.
• The resulting statistical estimators achieve optimal convergence rates.
• Simulation studies confirmed the method's superiority over competing approaches in terms of efficiency and speed.

Conclusions:

• The novel asympirical method provides a computationally efficient and accurate approach for smoothing spline ANOVA models with large datasets.
• The method offers significant advantages in statistical analysis of large-scale data, as evidenced by simulations and a real-world application in molecular dynamics.