Nonparametric estimation of a linear functional of the regression function in observation planning
The paper considers the estimation of the linear functional \(L(R)=\int_{T}R(t)d\mu\), where \(R(t)=M(X| t)=\int x P(dx| t)\) is the regression function, P(\(\cdot | t)\), \(t\in T\) is a family of conditional distributions on the line, and (T,\({\mathfrak A},\mu)\) is a measure space with finite measure \(\mu\). An observation plan \(t^{(n)}\) and an estimate \(\tilde L_ n\) based on \(t_ 1,X_ 1,...,t_ n,X_ n\) is constructed, such that the difference \[ \Delta_ n=M(\tilde L_ n-L(R))^ 2 \] is minimal in some asymptotic sense under various assumptions about the properties of observation noise.
scientific article; zbMATH DE number 3994764