Supercomputers for Monte Carlo Simulation: Cross-Validation versus Rao's Test in Multivariate Regression

摘要

Part I covers supercomputers, especially vector computers, which require thinking in vector mode. The mode is examined in the context of Monte Carlo experiments with regression models. The vector mode needs to exploit a specific dimension of the Monte Carlo experiment, namely its replicates. The resulting code computes Ordinary Least Squares estimates on a Cyber 205 in 2% of the time needed on a Vax 8700. For Generalized Least Squares estimates, however, the code runs slower on the Cyber 205 than on the VAX, if the regression model is small; for large models the CYBER 205 runs much faster. Part II covers regression models with dependent errors. To test the validity of the specified regression model, Rao (1959) generalized the F statistic for lack of fit, whereas Kleijnen (1983) proposed cross-validation using Student's t statistic combined with Bonferroni's inequality. An extensive Monte Carlo experiment compares these two methods. It then compares several confidence interval procedures for individual regression parameters.