Abstract: We consider the variable selection problem in regression models when the number of covariates is allowed to increase with the sample size. An approach of Zheng and Loh (1995) for the fixed design situation is extended to the case of random covariates. This yields a unified consistent selection criterion for both random and fixed covariates. By using t-statistics to order the covariates, the method requires much less computation than an all-subsets search. An application to autoregressive model selection with increasing order is given. The theory is supported by some simulation results.
Key words and phrases: Autoregressive processes, random covariates, t-statistic.