Optimal function-on-scalar regression over complex domains

Research output: Contribution to journalArticlepeer-review


In this work we consider the problem of estimating function-on-scalar regression models when the functions are observed over multi-dimensional or manifold domains and with potentially multivariate output. We establish the minimax rates of convergence and present an estimator based on reproducing kernel Hilbert spaces that achieves the minimax rate. To better interpret the derived rates, we extend well-known links between RKHS and Sobolev spaces to the case where the domain is a compact Rie-mannian manifold. This is accomplished using an interesting connection to Weyl’s Law from partial differential equations. We conclude with a numer-ical study and an application to 3D facial imaging.

Original languageEnglish (US)
Pages (from-to)156-197
Number of pages42
JournalElectronic Journal of Statistics
Issue number1
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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