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This paper evaluates state-of-the-art parametric and nonparametric approaches for the estimation of leaf chlorophyll content (Chl), leaf area index, and fractional vegetation cover from space. The parametric approach involves comparison of established and generic narrowband vegetation indices (VIs) and the Normalized Area Over reflectance Curve method, which calculates the continuum spectral region sensitive to Chl. However, as not all available bands take part in these spectral algorithms, it remains unclear whether optimal estimations are achieved. Alternatively, the nonparametric approach is based on Gaussian process (GP) techniques and allows inclusion of all bands. GP builds a nonlinear regression as a linear combination of spectra mapped to a high-dimensional space. Moreover, GP provides an indication of the most contributing bands for each parameter, a weight for the most relevant spectra contained in the training data set, and a confidence estimate of the retrieval. GP has previously demonstrated to be competitive in accuracy with support vector regression and neural networks. Results from hyperspectral Compact High Resolution Imaging Spectrometer data over the Spanish Barrax test site show that GP outperformed the VIs in assessing the vegetation properties when using at least four out of the 62 bands. GP identified most contributing bands in the red and red edge and, to a lower extent, in the blue and NIR parts of the spectrum. Since the proposed GP method is able to build robust relationships between the parameter of interest and only a few bands, it is a promising approach for multispectral data as well.