Photon-counting detectors with multi-bin pulse height analysis (PHA) are capable of extracting energy dependent information which can be exploited for material decomposition. Iterative decomposition algorithms have been previously implemented which require prior knowledge of the source spectrum, detector spectral response, and energy threshold settings. We experimentally investigated two material decomposition methods that do not require explicit knowledge of the source spectrum and spectral response. In the first method, the effective spectrum for each energy bin is estimated from calibration transmission measurements, followed by an iterative maximum likelihood decomposition algorithm. The second investigated method, first proposed and tested through simulations by Alvarez, uses a linearized maximum likelihood estimator which requires calibration transmission measurements. The Alvarez method has the advantage of being non-iterative. This study experimentally quantified and compared the material decomposition bias, as a percentage of material thickness, and standard deviation resulting from these two material decomposition estimators. Multi-energy x-ray transmission measurements were acquired through varying thicknesses of Teon, Delrin, and neoprene at two different flux settings and decomposed into PMMA and aluminum thicknesses using the investigated methods. In addition, a series of 200 equally spaced projections of a rod phantom were acquired over 360°. The multi-energy sinograms were decomposed using both empirical methods and then reconstructed using filtered backprojection producing two images representing each basis material. The Alvarez method decomposed Delrin into PMMA with a bias of 0.5-19% and decomposed neoprene into aluminum with a bias of less than 3%. The spectral estimation method decomposed Delrin into PMMA with a bias of 0.6-16% and decomposed neoprene into aluminum with a bias of 0.1-58%. In general, the spectral estimation method resulted in larger bias than the Alvarez method. Both methods demonstrated similar standard deviations of less than 1 mm. Both decomposition methods resulted in similar bias and standard deviation when comparing performance at the two flux levels. The results suggest preliminary feasibility of two empirical methods that use calibration measurements rather than prior knowledge of system parameters to estimate thicknesses of the basis materials.