|Scheipl, Fabian; Greven, Sonja (2016): Identifiability in penalized function-on-function regression models. Department of Statistics: Technical Reports, No.125|
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Regression models with functional responses and covariates constitute a powerful and increasingly important model class. However, regression with functional data poses well known and challenging problems of non-identifiability. This non-identifiability can manifest itself in arbitrarily large errors for coefficient surface estimates despite accurate predictions of the responses, thus invalidating substantial interpretations of the fitted models. We offer an accessible rephrasing of these identifiability issues in realistic applications of penalized linear function-on-function-regression and delimit the set of circumstances under which they are likely to occur in practice. Specifically, non-identifiability that persists under smoothness assumptions on the coefficient surface can occur if the functional covariate's empirical covariance has a kernel which overlaps that of the roughness penalty of the spline estimator. Extensive simulation studies validate the theoretical insights, explore the extent of the problem and allow us to evaluate their practical consequences under varying assumptions about the data generating processes. A case study illustrates the practical significance of the problem. Based on theoretical considerations and our empirical evaluation, we provide immediately applicable diagnostics for lack of identifiability and give recommendations for avoiding estimation artifacts in practice.
|Item Type:||Paper (Technical Report)|
|Faculties:||Mathematics, Computer Science and Statistics|
Mathematics, Computer Science and Statistics > Statistics
Mathematics, Computer Science and Statistics > Statistics > Technical Reports
|Subjects:||500 Science > 510 Mathematics|
|Deposited On:||22. Feb 2016 15:12|
|Last Modified:||22. Feb 2016 15:12|
Available Versions of this Item
Identifiability in penalized function-on-function regression models. (deposited 12. Jun 2012 12:14)
- Identifiability in penalized function-on-function regression models. (deposited 22. Feb 2016 15:12) [Currently Displayed]
- Identifiability in penalized function-on-function regression models. (deposited 11. Jun 2015 20:05)