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Wearable devices for continuous monitoring of electronic health increasedattention due to their richness in information. Often, inference is drawn fromfeatures that quantify some summary of the data, leading to a loss ofinformation that could be useful when one utilizes the functional nature of theresponse. When functional trajectories are observed repeated over time, it istermed longitudinal functional data. This work is motivated by the interest toassess the efficacy of a noninflammatory medication, meloxicam, on the dailyactivity levels of household cats with a pre-existing condition ofosteoarthritis under a crossover design. These activity profiles are recordedat a minute level by accelerometer over the entire study period. To thisaspect, we propose an orthogonal projection-based test pseudo generalized Ftest for significance of the functional treatment effect under a functionaladditive crossover model after adjusting for the carryover effect and otherbaseline covariates. Under mild conditions, we derive the asymptotic nulldistribution of the test statistic when the projection function for theunderlying Hilbert space is estimated from the data. In finite sample numericalstudies, the proposed test maintains the size, is powerful to detect thesignificance of the smooth effect of meloxicam, and is very efficient comparedto bootstrap-based alternatives.

PROLIFIC: Projection-based Test for Lack of Importance of Smooth Functional Effect in Crossover Design