A Non-Parametric Method for Imputing Censored Values below the Limit of Detection

Accurate imputation of censored data due to the limit of detection (LOD) is essential in many scientific fields. Existing imputation approaches typically rely on strict distributional assumptions or linear regression models, limiting their ability to capture complex non-linear relationships in multidimensional censored data. To address this limitation, we propose a non-parametric imputation method for censored data, termed NPIC, which iteratively imputes each censored variable using random forests and kernel density estimation (KDE) within a Gibbs sampling framework. Specifically, for each censored variable, NPIC treats it as the response and the remaining variables as predictors, trains a random forest model, computes the corresponding residuals, and estimates their density using KDE. This estimated residual density is then used to construct a truncated density, from which the expectation is calculated and used as the imputed value. Simulations on public datasets show that NPIC outperforms state-of-the-art methods. By integrating NPIC with MissForest, we develop NPICM, a unified non-parametric method for imputing both censored and missing values, and demonstrate its effectiveness on a real-world water quality dataset.