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.

中文翻译：

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具有检测限的功能数据均值函数的快速估计器

在许多关于疾病进展的研究中，生物标志物受到检测限的限制，因此信息缺失。当前的方法要么通过仅填充缺失观测值的检测限值来忽略该问题，要么应用全局方法来估计均值函数。后者对于密集数据来说是耗时的，并且获得的估计取决于整个观察到的区间，这可能是不现实的。我们将为受检测限制的不平衡稀疏和密集数据的均值函数提出新的估计器。我们将推导出估计量的渐近性质。我们将通过模拟将我们的方法与现有方法进行比较，并通过数据应用程序说明新方法。我们的方法似乎表现良好。对于密集数据，