Taylor approximation can be used to generate a linear approximation to a logistic ICC and a linear ability estimator. For a specific situation it will be shown to result in a special case of a Robbins-Monro item selection procedure for adaptive testing. The linear estimator can be used for the situation of zero and perfect scores when maximum likelihood estimation fails to come up with a finite estimate. It is also possible to use this estimator to generate starting values for maximum likelihood and weighted likelihood estimation. Approximations to the expectation and variance of the linear estimator for a sequence of Robbins-Monro item selections can be determined analytically.