We develop nonparametric smoothing for regression when both the predictor and the response variables are defined on a sphere of whatever dimension. A local polynomial fitting approach is pursued, which retains all the advantages in terms of rate optimality, interpretability and ease of implementation widely observed in the standard setting. Our estimates have a multi-output nature, meaning that each coordinate is separately estimated, within a scheme of a regression with a linear response. The main properties include linearity and rotational equivariance.
Nonparametric regression for spherical data / Marco Di Marzio; Agnese Panzera; Charles C. Taylor. - In: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION. - ISSN 0162-1459. - STAMPA. - 109:(2014), pp. 748-763. [10.1080/01621459.2013.866567]
Nonparametric regression for spherical data
PANZERA, AGNESE;
2014
Abstract
We develop nonparametric smoothing for regression when both the predictor and the response variables are defined on a sphere of whatever dimension. A local polynomial fitting approach is pursued, which retains all the advantages in terms of rate optimality, interpretability and ease of implementation widely observed in the standard setting. Our estimates have a multi-output nature, meaning that each coordinate is separately estimated, within a scheme of a regression with a linear response. The main properties include linearity and rotational equivariance.File | Dimensione | Formato | |
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