A least-squares identification method is studied that estimates a finite number of expansion coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized basis functions. The basis functions are orthogonal in H-2, and generalize the pulse, Laguerre and Kautz bases. One of their important properties is that, when chosen properly, they can substantially increase the speed of convergence of the series expansion. This leads to accurate approximate models with only a few coefficients to be estimated. Explicit bounds are derived for the bias and variance errors that occur in parameter estimates as well as in the resulting transfer function estimates.