Abstract
A new projection-based definition of quantiles in a multivariate setting is proposed. This approach extends in a natural way to infinite-dimensional Hilbert and Banach spaces. Sample quantiles estimating the corresponding population quantiles are defined and consistency results are obtained. Principal quantile directions are defined and asymptotic properties of the empirical version of principal quantile directions are obtained.
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Fraiman, R., Pateiro-López, B. (2011). Functional Quantiles. In: Ferraty, F. (eds) Recent Advances in Functional Data Analysis and Related Topics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2736-1_19
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DOI: https://doi.org/10.1007/978-3-7908-2736-1_19
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