Integrated data depth for smooth functions and its application in supervised classification

Abstract

This paper concerns depth functions suitable for smooth functional data. We suggest a modification of the integrated data depth that takes into account the shape properties of the functions.

This is achieved by including a derivative(s) into the definition of the suggested depth measures. We then further investigate the use of integrated data depths in supervised classification problems.

The performances of classification rules based on different data depths are investigated, both in simulated and real data sets. As the proposed depth function provides a natural alternative to the depth function based on random projections, the difference in the performances of these two methods are discussed in more detail.

Keywords

• Data depths
• Functional data
• Integrated data depths
• Supervised classification