Additive regression for non-Euclidean responses and predictors. (English) Zbl 1486.62109
Summary: Additive regression is studied in a very general setting where both the response and predictors are allowed to be non-Euclidean. The response takes values in a general separable Hilbert space, whereas the predictors take values in general semimetric spaces, which covers a very wide range of nonstandard response variables and predictors. A general framework of estimating additive models is presented for semimetric space-valued predictors. In particular, full details of implementation and the corresponding theory are given for predictors taking values in Hilbert spaces and/or Riemannian manifolds. The existence of the estimators, convergence of a backfitting algorithm, rates of convergence and asymptotic distributions of the estimators are discussed. The finite sample performance of the estimators is investigated by means of two simulation studies. Finally, three data sets covering several types of non-Euclidean data are analyzed to illustrate the usefulness of the proposed general approach.
MSC:
| 62G08 | Nonparametric regression and quantile regression |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62R30 | Statistics on manifolds |
Keywords:
additive models; compositional data; density-valued data; directional data; functional data; Hilbert spaces; non-Euclidean data; Riemannian manifolds; shape data; smooth backfittingSoftware:
gamairReferences:
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