|Scheipl, Fabian; Greven, Sonja (11. June 2015): Identifiability in penalized function-on-function regression models. Department of Statistics: Technical Reports, No.125|
This is the latest version of this item.
Regression models with functional covariates for functional responses constitute a powerful and increasingly important model class. However, regression with functional data poses challenging problems of non-identifiability. We describe these identifiability issues in realistic applications of penalized linear function-on-function-regression and delimit the set of circumstances under which they arise. Specifically, functional covariates whose empirical covariance has lower effective rank than the number of marginal basis function used to represent the coefficient surface can lead to unidentifiability. Extensive simulation studies validate the theoretical insights, explore the extent of the problem and allow us to evaluate its practical consequences under varying assumptions about the data generating processes. Based on theoretical considerations and our empirical evaluation, we provide easily verifiable criteria for lack of identifiability and provide actionable advice for avoiding spurious estimation artifacts. Applicability of our strategy for mitigating non-identifiability is demonstrated in a case study on the Canadian Weather data set.
|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:||11. Jun 2015 20:05|
|Last Modified:||11. Jun 2015 20:05|
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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)
- Identifiability in penalized function-on-function regression models. (deposited 11. Jun 2015 20:05) [Currently Displayed]