Description: The Minimum Absolute Deviations (MAD) is a statistical method used to fit models to observed data by minimizing the sum of the absolute deviations between the observed values and the values predicted by the model. This approach is particularly useful in situations where the data may contain outliers; compared to methods that minimize squared errors, MAD is less sensitive to these extreme values. Essentially, the goal of MAD is to find a function that fits the data in such a way that the sum of the absolute differences between the actual values and the estimated values is as small as possible. This method is applied in various fields, including economics, engineering, and social sciences, where robust data analysis is required. MAD can be used in both linear and nonlinear regressions and is a valuable tool for modeling and prediction, providing an effective alternative to other fitting methods that may be more vulnerable to the influence of outlier data.
History: The concept of Minimum Absolute Deviations dates back to statistical work in the 20th century, where more robust methods for model fitting were sought. Although the least squares method was widely used, it was recognized to be sensitive to outliers, leading to the exploration of alternatives such as MAD. Over the years, this approach has evolved and been integrated into various statistical techniques and optimization algorithms.
Uses: Minimum Absolute Deviations are used in multiple disciplines, including economics for demand model estimation, in engineering for curve fitting in experiments, and in social sciences for survey analysis. Their ability to handle outlier data makes them especially valuable in contexts where data quality may be variable.
Examples: A practical example of Minimum Absolute Deviations is its application in predicting housing prices, where prices may be affected by outlier factors such as sales of properties under exceptional conditions. Another example is in traffic data modeling, where MAD can help fit models predicting vehicle flow without being influenced by unusual events.
