A Note on Kernel Regression with Several Bandwidth Selection Methods in Software Reliability Prediction

In this note, we consider a data-driven approach to software reliability prediction based on kernel regression, where the software fault-count process during system testing is modeled directly from observed fault data without imposing a strict parametric distributional assumption. This perspective is particularly useful in practical software testing environments, where the underlying fault-generation mechanism is often complex, time-varying, and difficult to characterize accurately by a single predefined stochastic model. To address this issue, a non-parametric prediction framework is developed by employing kernel regression with several bandwidth selection methods, with the aim of investigating how bandwidth choice influences prediction accuracy, estimation stability, and overall model robustness. Since the bandwidth plays a central role in controlling the bias-variance tradeoff in kernel-based estimation, inappropriate bandwidth selection may lead to over-smoothing or under-smoothing, thereby degrading predictive performance in long-term software fault prediction. In the proposed framework, multiple bandwidth selection strategies are examined and compared under the same prediction setting, and their predictive behaviors are analyzed from both estimation and forecasting perspectives. Through comparative analysis, the proposed approach provides useful insights into the role of bandwidth selection in software fault prediction and offers practical guidance for software reliability evaluation when distributional knowledge is incomplete or uncertain. The results also suggest that careful bandwidth selection is essential for improving the applicability of kernel-based reliability prediction methods in real-world software testing data.