ABSTRACT
Nonparametric regression was treated briefly in Chapter 2.3. The ideas carry over to the general case as follows. The basic model is
X(t) = f (t)+σZ(t), 0≤ t ≤ 1, (7.1)
where f : [0,1]→ R is a function and Z(t) is the standardized noise which is often taken to be Gaussian white noise. Given data (t,x)n = (t j,x(t j)), j = 1, . . . ,n the problem is to produce one or more functions fn and values σn such that the model with f = fn and σ = σn is an adequate approximation of the data.
