Infinite Dimensional Problems

Abstract

Many nonparametric estimation problems can be regarded as involving estimation of infinite dimensional parameters. This is the situation, for example, in the neuronal membrane potential model $dV(t) = ( - pV(t) + \theta (t))dt + dM(t)$ discussed earlier in Section 2.6 with parameters held constant, if changes in θ(t) over the recording interval 0 ≤ t ≤ T are important and the function needs to be estimated. Both the situation where n replica trajectories of {V(t), 0 ≤ t ≤ T are observed and n → ∞ or one trajectory is observed and T → ∞ are of interest but most of the established results deal with the former case.