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- Title
High leverage detection in general functional regression models with spatially correlated errors.
- Authors
Romano, Elvira; Giraldo, Ramón; Mateu, Jorge; Diana, Andrea
- Abstract
The presence of curves that deviate markedly from the core of a set of curves can greatly affect inference and forecasting in a functional regression model. Thus their detection is key to increase the accuracy of the required estimates. This work introduces the concepts of high leverage in general functional regression models with independent and spatially correlated errors. The projection matrix, also known as Hat matrix, plays a crucial role in classical model diagnosis, since it provides a measure of leverage. We propose a generalisation of the projection matrix in both the functional and the spatial functional frameworks under two settings, when the response variable is a scalar, and when it is a function itself, the so‐called total model. Commonly used influence measures are also proposed as functions of the generalised functional leverages and residuals. An application of the proposed procedures for investigating the effect of outliers on the relationship between transformation of the banking industry and the size of cooperative banks in Italy over a period of 14 years is presented.
- Subjects
ITALY; REGRESSION analysis; COOPERATIVE banking industry
- Publication
Applied Stochastic Models in Business & Industry, 2022, Vol 38, Issue 1, p169
- ISSN
1524-1904
- Publication type
Article
- DOI
10.1002/asmb.2654