Vector Lattice Data Analysis: Fitting and Model Uncertainty
Christos E. Kountzakis, Amani Almohaimeed · Journal of Advances in Applied & Computational Mathematics · 2025
Functional data analysis (FDA) is a popular research area of data analysis that is well-suited for modeling complex data structures such as time series data and images. In Linear Regression models, the random variables are often described using a finite--dimensional vector space, under the assumption that the random variables are represented by a finite set of parameters. FDA allows us to model random variables as functions. This can lead to a more flexible and expressive approach to the statistical model. Within FDA, the specific paper investigates the potential of vector lattices to enhance model flexibility and address model uncertainty. The limitations of finite-dimensional vector spaces in capturing the complexities of real-world random variables are discussed. An investigation is conducted into the concept of Vector Lattice Linear Regression Models (VLLM), highlighting their ability to effectively handle model uncertainty.