2023/12/12 by Chi Zhang, Zhang, Chi, Peijun Sang +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2312.07727
openalex publication_date 2023/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a novel test procedure for comparing mean functions across two groups within the reproducing kernel Hilbert space (RKHS) framework. Our proposed method is adept at handling sparsely and irregularly sampled functional data when observation times are random for each subject. Conventional approaches, which are built upon functional principal components analysis, usually assume a homogeneous covariance structure across groups. Nonetheless, justifying this assumption in real-world scenarios can be challenging. To eliminate the need for a homogeneous covariance structure, we first develop a linear approximation for the mean estimator under the RKHS framework; this approximation is a sum of i.i.d. random elements, which naturally leads to the desirable pointwise limiting distributions. Moreover, we establish weak convergence for the mean estimator, allowing us to construct a test statistic for the mean difference. Our method is easily implementable and outperforms some conventional tests in controlling type I errors across various settings. We demonstrate the finite sample performance of our approach through extensive simulations and two real-world applications.