We propose a combination of portable X-ray fluorescence (pXRF) and chemometrics to discriminate between Mesoamerican obsidian sources and to assign archaeological artifacts of unknown origin to their respective deposits using a procedure that does not require any type of calibration or reference standards. A set of 109 samples of known origin and a total of 257 samples of unknown origin were analyzed with a portable XRF spectrometer. The resultant spectra were used as spectral signatures for the chemometric data analysis. First, we applied spectral pre-treatment techniques, such as CluPA algorithm for peak alignment and the Savitzky-Golay and Extended Multiplicative Signal Correction for data smoothing and noise removal, combined with methods for the selection of a spectral range containing the variables with the most relevant information (iPLS and). The full spectrum of the obsidian samples was divided into 20 subintervals, fitting a local regression model (PLS) to each subinterval. The performance was evaluated by the Root Mean Square Error of Cross-Validation, the Root Mean Square Error of Prediction and the correlation coefficient. The selected spectral regions were then analyzed with ROBPCA algorithm for the discrimination of outliers and the projection of the observations in the PCA space. For the classification, we propose a robust procedure (RSIMCA) which is based on a ROBPCA method for high-dimensional data. The classification rules were obtained by using the orthogonal and the score distances, from which it is possible to distinguish samples that belong to a given group. Using the proposed methodology, we were able to provide evidence about which variables were meaningful for the classification and provided information about group membership or provenance. This approach proves to be a valid technique for the quantitative analysis of XRF spectra.