Survival analysis using Mahalanobis distance in Kernels of the Beran estimator

Survival analysis is critical for modeling time-to-event data across medicine, engineering, and economics. The Beran estimator serves as an efficient nonparametric tool for estimating conditional survival functions under censoring. However, the conventional Beran estimator relies on the Euclidean distance for kernel weighting, a metric that fails to account for heterogeneous scales and correlations among covariates. This limitation can result in suboptimal weighting when features exhibit multicollinearity or varying measurement units. To address this, we propose the M-Beran estimator, a generalized formulation that incorporates the Mahalanobis distance into the kernel smoothing scheme. This modification ensures scale invariance and leverages the underlying correlation structure of the feature space, transforming the kernel into an elliptically symmetric form. We evaluate the proposed method through numerical experiments on real-world survival datasets. Results demonstrate that the M-Beran estimator outperforms the conventional Euclidean-distance-based Beran estimator, offering improved predictive accuracy.