1. A method for making optimal estimates of linearity metrics of an analog-to-digital converter, comprising: constructing a statistical model of transition code voltages of the analog-to-digital converter based on application of a test input signal to a plurality of training analog-to-digital converters of like kind and measurements of the transition code voltages of said plurality of training analog-to-digital converters, said statistical model being adapted to produce an estimate of the transition code voltages for an individual analog-to-digital converter in response to a plurality of scaling inputs; generating said scaling inputs by applying said test signal as an input to said individual analog-to-digital converter, measuring the transition code voltages thereof, and computing a least-squares estimate of said scaling inputs given said measured transition code voltages; and applying said generated scaling inputs to said statistical model to produce a set of estimated transition code voltages of said individual analog-to-digital converter that are more accurate than said measured transition code voltages thereof.