Experimental studies often fail to appropriately account for the number of collected samples within a fixed time interval for functional responses. Data of this nature appropriately falls under an Infill Asymptotic domain that is constrained by time and not considered infinite. Therefore, the sample size should account for this infill asymptotic domain. This paper provides general guidance on selecting an appropriate size for an experimental study for various simple linear regression models and tuning parameter values of the covariance structure used under an asymptotic domain, an Ornstein-Uhlenbeck process. Selecting an appropriate sample size is determined based on the percent of total variation that is captured at any given sample size for each parameter. Additionally, guidance on the selection of the tuning parameter is given by linking this value to the signal-to-noise ratio utilized for power calculations under design of experiments.

翻译：实验研究在处理固定时间间隔内收集的功能性响应样本数量时，常未能充分考虑其特性。这类数据本质上属于受时间约束而非无限范围的填充渐近域。因此，样本量的确定需纳入该填充渐近域的特征。本文针对多种简单线性回归模型及在渐近域（Ornstein-Uhlenbeck过程）中使用的协方差结构调谐参数值，提供了实验研究中样本量选择的一般性指导。样本量的合理选择基于各参数在给定样本量下所能捕获的总变异百分比。此外，通过将调谐参数值与实验设计下功效计算中使用的信噪比建立关联，给出了该参数的选择建议。