As data becomes increasingly complex, detecting anomalies or deviations in data has become a crucial task in many industries, including finance, healthcare, and manufacturing. One common approach to anomaly detection is the Hotelling approach, which relies on multivariate statistical analysis to identify observations that deviate from the norm.

The Hotelling approach is a powerful tool for detecting anomalies in data, especially when there are multiple variables at play. It involves creating a statistical model of the data and then comparing new observations against that model to identify any significant deviations.

One way to visualize the data and the deviations is through Principal Component Analysis (PCA). PCA is a technique used to reduce the dimensionality of large datasets, while retaining as much of the original variation as possible. By applying PCA to the dataset, we can transform the data into a set of new, uncorrelated variables called principal components. These principal components can then be plotted on a graph, allowing us to visualize the relationships between the variables and the deviations from the norm.

To estimate the contribution of variables to the anomaly or deviation moments, we can use the loadings of the principal components. The loadings represent the degree to which each variable contributes to each principal component. By examining the loadings of the principal components, we can identify which variables are contributing the most to the deviations from the norm.

It's worth noting that while the Hotelling approach is a powerful tool for detecting anomalies, it's not foolproof. There are always false positives and false negatives, so it's important to take a cautious approach when interpreting the results. Nevertheless, with careful application, the Hotelling approach can be a valuable addition to the anomaly detection toolkit of any data scientist or analyst.