Robust Estimation of Experimental Data with Gross Errors Using Least Absolute Deviations Method

In experimental datasets, the presence of gross errors necessitates the application of robust estimation methods to enhance data analysis accuracy. The Least Absolute Deviations (LAD) method serves as an effective robust estimation technique that minimizes the sum of absolute deviations rather than squared residuals. This approach reduces the influence of outlier data points through L1-norm optimization, which can be implemented using linear programming techniques or iteratively reweighted least squares algorithms. The method significantly improves both data accuracy and interpretability by providing median-based estimators that are less sensitive to extreme values compared to traditional least squares. For practical implementation, key functions like `fmincon` in MATLAB or `scipy.optimize.linprog` in Python can solve the optimization problem numerically. Consequently, the LAD method proves particularly valuable for experimental datasets contaminated with gross errors, offering superior robustness in statistical inference while maintaining computational efficiency through convex optimization frameworks.