The overall thrust of the research is to provide a nonparmetric alternative to current parametric approaches used in response surface methodology. The nonparametric methodology is based on kernel estimators. A test will be developed for the validity of the general additive model against a nonparametric alternative. In the case of a semiparametric model which models which models the deterministic part of the relationship between a response variable and several covariates, some covariates will be included in a parametric portion and the remaining covariates in a nonparametric portion. Then a test will be developed for the validity of the postulated semiparametric model against a nonparametric alternative. In choosing bandwidths for kernel estimates of a regression function, an analysis and method for choosing the optimal number of points to leave out of a cross validation type procedure will be developed assuming a pilot estimate of the unknown regression function is given.
