Speaker
Description
Functional data analysis (FDA) has become increasingly popular in medical biometry and statistics. It is often appropriate to model observations by smooth curves or functions for example in the situation of observations that are sampled quite dense over time or space or in case of high-dimensional repeated measurements as FDA methods allow a flexible modelling. Furthermore they does not assume a certain correlation structure between sampled cases or time points nor equally spaced time points. Despite many methodological development in the last few years, there are still methodologically unsolved problems. One of them is missingness in context of functional data.
That is why we present a method to deal with testing in the presence of missing values in a functional matched pairs design. by adapting the approach of [1] for functional data. The method assumes a missing completely at random (MCAR) mechanism and works without any distributional or heteroscedasticity assumption. Two permutation approaches were used to realise the testing in the presence of missing values and to reach a good small sample performance. We compare the new method with the bootstrap-based approach of [2] and with the imputation methods of [3].
[1] Amro, L., & Pauly, M. (2016). Permuting incomplete paired data: A novel exact and asymptotic correct randomization test. Journal of Statistical Computation and Simulation, 87(6), 1148–1159.
[2] Crainiceanu, C. M., Staicu, A.-M., Ray, S., & Punjabi, N. (2012). Bootstrap-based inference on the difference in the means of two correlated functional processes. Statistics in Medicine, 31(26), 3223–3240.
[3] Jang, J. H., Manatunga, A. K., Chang, C., & Long, Q. (2021). A Bayesian multiple imputation approach to bivariate functional data with missing components. Statistics in Medicine, 40(22), 4772–4793.
53573501324