New Pilot-Study Design in Functional Data Analysis

TL;DR

This paper introduces a new framework and search algorithm for designing pilot studies in functional data analysis, improving data collection efficiency when measurements are costly or limited.

Contribution

It presents a novel approach to pilot-study design that enhances trajectory recovery and future planning, addressing a previously overlooked aspect in functional data analysis.

Findings

Outperforms existing design methods in simulations

Demonstrates effectiveness with real data application

Supports accurate trajectory reconstruction with limited measurements

Abstract

Efficient data collection is essential in applied studies where frequent measurements are costly, time-consuming, or burdensome. This challenge is especially pronounced in functional data settings, where each subject is observed at only a few time points due to practical constraints. Most existing design approaches focus on selecting optimal time points for individual subjects, typically relying on model parameters estimated from a pilot study. However, the design of the pilot study itself has received limited attention. We propose a framework for constructing pilot-study designs that support both accurate trajectory recovery and effective planning of future designs. A search algorithm is developed to generate such high-quality pilot-study designs. Simulation studies and a real data application demonstrate that our approach outperforms commonly used alternatives, highlighting its value in resource-limited settings.