Residual-Based Subdata Selection for Local Regression and Its Extension to Partial Linear Model

Thomas M. Menino Convention & Exhibition Center 

The rapid growth of data has introduced considerable computational challenges in statistical analysis. This study addresses this issue in local linear regression through representative subdata selection to reduce the computational burden, then extends the method to partial linear models. For local linear regression, a residual-based subdata selection (RESS) method is introduced. RESS yields a lower asymptotic mean squared error than existing methods in a neighborhood where the absolute asymptotic bias is largest. For partial linear models, an integrated estimation approach, termed IBRESS, combines RESS for the nonlinear component with information-based optimal subdata selection (IBOSS) for the linear component. IBRESS leverages the strengths of both methods and satisfies two theoretical properties: (i) similar to IBOSS, the convergence rate of the linear component depends on the full data size; and (ii) the nonlinear component retains the asymptotic properties of RESS. Simulation studies demonstrate that IBRESS reduces computational cost while maintaining estimation accuracy.

Local linear regression

Subdata selection

Partial linear model

Nonparametric regression

L1 convergence 

Section on Nonparametric Statistics