Nonparametric Estimates of Biological Transducer Functions

Abstract

An effective method for estimating a transducer function from a set of biological data is local fitting with bootstrap bandwidth selection. The method overcomes many of the problems with parametric regression. Bootstrap local fitting can be applied to a range of biological data, including the photoreceptor voltage response in the turtle retina, feedback current response in the goldfish retina, auditory-nerve spike rate in the guinea pig, frequency-of-seeing performance in a human patient with glaucoma and a psychometric function for a normal human observer performing an image-discrimination task. The bootstrap method enables the optimal or close-to-optimal estimate of the bandwidth in the named applications. Another use is for the ready estimation of simultaneous confidence intervals wherein the simplest estimates can be derived from the empirical centiles of the bootstrap samples. In the above applications, local fitting provided an excellent description of data where a valid parametric model was unknown. Local fitting also produced a good description that preserved monotonicity even when the response was a complicated function, as with the experiment with human discrimination of image approximations. Results are also identical where local fits using the wild bootstrap were obtained. Bootstrap also has the possibility for cross-validation and produce an accurate estimate of a function, preserving the expected critical features and asymptotic behavior at small and large stimulus levels.