The sea state bias (SSB) affecting altimetric measurements of the sea surface height (SSH) is classically estimated using empirical parametric models. The model parameters are determined to minimize the variance of the SSH differences at crossover points or along collinear tracks. It is shown here that so-calibrated models are not true least squares approximations of the SSB. Simulations indicate that the difference from a true least squares solution is typically a few millimeters to a few centimeters, varying with sea state. This difference proves to be the result of the inevitably imperfect specification of the model's parametric form, which corrupts the calibration process when performed on SSH differences rather than directly on SSH measurements. To avoid specification of a parametric form, we present a new nonparametric version of the SSB estimation problem and propose a general solution based on the statistical technique of kernel smoothing. This solution is then used to obtain the first fully nonparametric estimate of the TOPEX altimeter SSB as a function of both the wind speed and the wave height. The obtained estimate, though based on a limited data set, proves to be better than those obtained with the standard parametric SSB models featured in the TOPEX-POSEIDON Geophysical Data Records. The improvement is most significant in middle- and high-latitude oceans. ¿ 1998 American Geophysical Union