Asymptotic Optimality for Cₚ, CL, Cross-Validation and Generalized Cross-Validation: Discrete Index Set

Key Points

• This research aims to analyze the asymptotic behaviors and optimality conditions of various data-driven techniques for selecting linear estimates.
• Studied asymptotic behaviors of methods such as C_p, C_L, cross-validation, and generalized cross-validation.
• Derived conditions for demonstrating asymptotic optimality.
• Explored applications in nearest-neighbor nonparametric regression and model selection.
• Demonstrated conditions under which cross-validation and generalized cross-validation achieve asymptotic optimality.
• Showed that cross-validation methods connect closely to C_L methods.
• Concluded with potential applications enhancing estimation accuracy in selected models.

Abstract