Talks

New Pilot Study Designs on Functional Data Analysis

Ping-Han Huang and Ming-Hung Kao

Recent years have seen many studies on the analysis of noisy, sparse functional data that are collected at sparse, irregularly spaced time points. In contrast to the existing work, our study focuses on formulating a good pilot-study design to facilitate identifying optimal designs for future data. We propose a pilot-study design that helps to find the best time points for collecting a high-quality pilot data set to allow experimenters to identify optimal designs for future subjects. The proposed pilot-study design also provides a good statistical efficiency in studying the random functions involved in the pilot study. A search algorithm is developed to generate such pilot-study designs and bring convenience for augmenting an existing design with additional subjects. We further demonstrate the usefulness of our designs by comparing with balanced incomplete block designs and random designs. Our simulation studies show that our designs yield better performance than the competing designs. In practice, it is particularly useful for generating informative pilot data set that gives promising preliminary results and attracts further investments in developing full-scale studies.

Pilot Study Designs for Sparse Functional Data

Ping-Han Huang and Ming-Hung Kao

In sparse functional data analysis (SFDA), the number of repeated measures per subject is often limited by practical constraints such as costs. In light of this issue, a number of approaches have been developed to find (locally) optimal designs to help increase the efficiency of SFDA. The success of these design methods greatly hinges on the accurate prior information from pilot studies. However, the selection of a good pilot study design remains unclear. The aim is to fill this gap by proposing new hybrid designs that combine some combinatorial designs with a 'notorious' type of FDA designs. Through simulation studies, we demonstrate that our proposed designs can outperform the widely used simple random designs to facilitate the use of previously developed locally optimal design approaches.