SEMI-RECURSIVE KERNEL ESTIMATION OF FUNCTIONS
OF DENSITY FUNCTIONALS AND THEIR DERIVATIVES
ann kitayeva, gennady koshkin
A class of semi-recursive kernel type estimates of
functions depending on multivariate density functionals and their
derivatives is considered. The piecewise smoothed approximations
of these estimates are proposed. The convergence with probability
one of the estimates is proved. The main parts of the asymptotic
mean square errors of the estimates are found. The examples of
estimation of the production function, the marginal productivity and the
marginal rate of technical substitution of inputs are given.