MATLAB Implementation of Bootstrap Source Code

Implementing the Bootstrap method in MATLAB is a widely used statistical technique that primarily generates multiple subsets through resampling with replacement from an original dataset. This method proves particularly valuable for statistical inference, model validation, and uncertainty estimation. The fundamental concept of Bootstrap involves repeated sampling from the original dataset to create numerous new sample sets. Each subset typically matches the original dataset's size, but due to the replacement sampling approach, certain data points may appear multiple times while others might be omitted entirely. Key implementation steps for Bootstrap include: - Randomly selecting N data points from the original dataset (where N equals the original dataset size) - Allowing repeated selection of the same data point to ensure independent and uniformly distributed sampling - Repeating this process multiple times to generate numerous subsets for subsequent analysis or statistical computation In MATLAB, built-in random number generation functions like `randsample` or `datasample` can efficiently implement Bootstrap sampling. The `randsample` function allows weighted sampling with replacement options, while `datasample` provides more comprehensive data sampling capabilities including stratification support. This approach is especially suitable for small-sample data analysis, offering more robust estimates compared to traditional parametric methods. Typical Bootstrap applications include confidence interval calculation, machine learning model stability assessment, and data distribution simulation. Since it doesn't rely on strict distribution assumptions, Bootstrap is particularly practical in nonparametric statistics. For implementation, MATLAB's statistical toolbox provides optimized functions that handle sampling efficiency and memory management, making it suitable for large-scale resampling operations.