One or more cardiovascular parameters is estimated as a function of the arterial pressure waveform, in particular, using at least one statistical moment of pressure waveform having an order greater than one. Arterial compliance, the exponential pressure decay constant, vascular resistance, cardiac output, and stroke volume are examples of cardiovascular parameters that can be estimated using various aspects of the invention. In one embodiment of the invention, not only are the first four moments (mean, standard deviation, skewness, and kurtosis) of the pressure waveform used to estimate the cardiovascular parameter(s) of interest, but also heart rate, statistical moments of a set of pressure-weighted time values, and certain anthropometric patient measurements such as age, sex, body surface area, etc.