We study the estimation of the mean function of a continuous-time stochastic process andits derivatives. The covariance function of the process is assumed to be nonparametric andto satisfy mild smoothness conditions. Assuming that n independent realizationsof the process are observed at a sampling design of size N generated by a positivedensity, we derive the asymptotic bias and variance of the local polynomial estimator asn,Nincrease to infinity. We deduce optimal sampling densities, optimal bandwidths, andpropose a new plug-in bandwidth selection method. We establish the asymptotic performanceof the plug-in bandwidth estimator and we compare, in a simulation study, its performancefor finite sizes n,N to the cross-validation and the optimalbandwidths. A software implementation of the plug-in method is available in the Renvironment.

Four indices of visual performance were measured in control macaques and in macaques that had been exposed to monomeric acrylamide, a neurotoxicant that preferentially damages P retinal ganglion cells. Morphological examination of the retina and visual pathways of these monkeys showed virtually complete loss of P ganglion cells over a region extending to at least 40 deg from the fovea, and relative sparing of M ganglion cells. The four tests examined visual functions for which the visual pathway from P ganglion cells might be of great importance: visual acuity, contrast discrimination, hyperacuity, and shape discrimination.

In the acrylamide-dosed monkeys, visual acuity was reduced slightly more than fourfold, a somewhat larger reduction than that seen previously after ibotenic-acid lesions of the P pathway in the geniculate. The residual acuity was in good agreement with the Nyquist frequency calculated from the density of ON or OFF M ganglion cells. Contrast increment thresholds were elevated for the dosed monkeys only in one of the two conditions tested. The elevation was found only under those spatiotemporal conditions for which we have previously shown that contrast thresholds are increased by acrylamide exposure, and was most marked at low background contrasts. Vernier acuity was elevated in one dosed monkey, but not affected in a second monkey that also had severe loss of P ganglion cells. Finally, we found no effect of acrylamide exposure on the number of training trials required to learn simple or complex shape discriminations. These results support previous findings in showing that the P pathway mediates visual acuity, and they show that several other important aspects of visual perception are not exclusively dependent on the P pathway.