Methods and applications of the generalized partially linear single-index model.

摘要

The central topic of this thesis is the estimation of parameters of the generalized partially linear single-index model. Two optimization procedures are presented and an S-Plus program based on these procedures is compared to a program by Wand in a simulation setting. The results from these simulations indicate that the estimates for the new procedures are as good, if not better, than Wand's. Other details concerning the generalized partially linear single-index model are worked out including the variance of the estimates. As well, the results from one set of simulations indicate that the likelihood ratio test is the preferred criterion for testing that one of the elements of alpha is equal to zero. The generalized partially linear single-index model is applied to a water quality data set and the results indicate an interesting relationship between gastrointestinal illness and turbidity (cloudiness) of drinking water.