A novel ranked <i>k</i> -nearest neighbors algorithm for missing data imputation

Missing data is a common problem in many domains that rely on data analysis. The <i>k</i> Nearest Neighbors imputation method has been widely used to address this issue, but it has limitations in accurately imputing missing values, especially for datasets with small pairwise correlations and small values of <i>k</i>. In this study, we proposed a method, Ranked <i>k</i> Nearest Neighbors imputation that uses a similar approach to <i>k</i> Nearest Neighbor, but utilizing the concept of Ranked set sampling to select the most relevant neighbors for imputation. Our results show that the proposed method outperforms the standard <i>k</i> nearest neighbor method in terms of imputation accuracy both in case of Missing Completely at Random and Missing at Random mechanism, as demonstrated by consistently lower MSIE and MAIE values across all datasets. This suggests that the proposed method is a promising alternative for imputing missing values in datasets with small pairwise correlations and small values of <i>k</i>. Thus, the proposed Ranked <i>k</i> Nearest Neighbor method has important implications for data imputation in various domains and can contribute to the development of more efficient and accurate imputation methods without adding any computational complexity to an algorithm.