ADDITIVE REGRESSION FOR NON-EUCLIDEAN RESPONSES AND PREDICTORS
| Autor: | Ingrid Van Keilegom, Byeong U. Park, Jeong Min Jeon |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Statistics & Probability MODELS LOCAL POLYNOMIAL REGRESSION shape data symbols.namesake smooth backfitting Riemannian manifolds density-valued data Non-Euclidean geometry Convergence (routing) Range (statistics) Applied mathematics Additive model NONPARAMETRIC REGRESSION functional data Mathematics Hilbert spaces Science & Technology Hilbert space Estimator non-Euclidean data Regression compositional data ERRORS-IN-VARIABLES KERNEL DENSITY-ESTIMATION Physical Sciences directional data MANIFOLDS symbols Statistics Probability and Uncertainty Backfitting algorithm Additive models |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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