Sample Size Selection under an Infill Asymptotic Domain

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.