The purpose of the present paper is to investigate a class of spherical functional autoregressive processes in order to introduce and study LASSO (Least Absolute Shrinkage and Selection Operator) type estimators for the corresponding autoregressive kernels, defined in the harmonic domain by means of their spectral decompositions. Some crucial properties for these estimators are proved, in particular, consistency and oracle inequalities.

中文翻译：

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球形自回归过程的LASSO估计

本文的目的是研究一类球面函数自回归过程，以便为相应的自回归核引入LASSO（最小绝对收缩和选择算子）类型的估计器，并通过其光谱分解在谐波域中对其进行定义。 。证明了这些估计量的一些关键属性，尤其是一致性和预言性不等式。