Asymptotic optimality and efficient computation of the leave-subject-out cross-validation

TL;DR

This paper establishes the asymptotic optimality of leave-subject-out cross-validation for penalized spline models in longitudinal data and introduces an efficient algorithm for its computation.

Contribution

It proves the asymptotic optimality of leave-subject-out CV and develops a Newton-type algorithm for efficient penalty parameter selection.

Findings

Leave-subject-out CV is asymptotically equivalent to minimizing squared error.

The proposed algorithm efficiently computes optimal penalty parameters.

Simulations and real data confirm the method's effectiveness.

Abstract

Although the leave-subject-out cross-validation (CV) has been widely used in practice for tuning parameter selection for various nonparametric and semiparametric models of longitudinal data, its theoretical property is unknown and solving the associated optimization problem is computationally expensive, especially when there are multiple tuning parameters. In this paper, by focusing on the penalized spline method, we show that the leave-subject-out CV is optimal in the sense that it is asymptotically equivalent to the empirical squared error loss function minimization. An efficient Newton-type algorithm is developed to compute the penalty parameters that optimize the CV criterion. Simulated and real data are used to demonstrate the effectiveness of the leave-subject-out CV in selecting both the penalty parameters and the working correlation matrix.