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We consider inference for the mean and covariance functions of covariateadjusted functional data using Local Linear Kernel (LLK) estimators. By meansof a double asymptotic, we differentiate between sparse and dense covariateadjusted functional data - depending on the relative order of m (thediscretization points per function) and n (the number of functions). Oursimulation results demonstrate that the existing asymptotic normality resultscan lead to severely misleading inferences in finite samples. We explain thisphenomenon based on our theoretical results and propose finite-samplecorrections which provide practically useful approximations for inference insparse and dense data scenarios. The relevance of our theoretical results isshowcased using a real-data application.

Inference for Sparse and Dense Functional Data with Covariate Adjustments