Optimal designs for nonparametric kernel regression (Q1060797)

We consider the fixed design regression model \(Y_ i=g(t_ i)+\xi_ i\), \(i=1,...,n\), where \(\xi_ i\) are (not necessarily i.i.d.) noise variables, \(t_ i\) constitute the design points where nonrepeatable measurements are to be taken and \(Y_ i\) are the observations from which g and its derivatives are to be estimated. The dependency of the integrated mean squared error of two different types of kernel estimates on the design \(\{t_ 1,...,t_ n\}\) is established. This allows the derivation of asymptotically optimal designs.