ABSTRACT
This chapter examines the functions available in S-PLUS for numerical optimisation in the context of both nonlinear regression and maximum likelihood estimation. To illustrate the former, a data set showing times in seconds recorded by the winners of the men’s Olympic 1500-m event from 1900 to 2000 is used. Interest here centres on fitting a particular regression model to the data that might be used to predict future winning times, and the ultimate time achievable. As an example of the application of maximum likelihood estimation in S-PLUS, the chapter shows estimation of the parameters of a normal mixture distribution fitted to another dataset. These data consist of the waiting times between successive eruptions of the Old Faithful geyser in Yellowstone National Park, Wyoming, USA. There were 300 eruptions observed in the period of observation; so the dataset contains 299 waiting times measured in minutes.
