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Fast estimators for the mean function for functional data with detection limits

In many studies on disease progression, biomarkers are restricted by detection limits, hence informatively missing. Current approaches either ignore the problem by just filling in the value of the detection limit for the missing observations or apply a global approach for estimation of the mean function. The latter is time‐consuming for dense data, and the obtained estimate depends on the whole observed interval which might not be realistic. We will propose novel estimators for the mean function for both unbalanced sparse and dense data subject to the detection limit. We will derive the asymptotic properties of the estimators. We will compare our methods to the existing methods via simulations and illustrate the new methods with a data application. Our methods appear to perform well. For dense data, the approximation methods are computationally much faster than existing methods.