Central to obtaining reliable statistical inference from observed or modeled atmospheric time series is the construction of confidence intervals (CIs) for their parameters. The target coverage probability of these CIs it is attained only if the assumptions underlying the method for the CI construction are met. Conventional statistical methods, however, are based on strong assumptions about the data generating mechanisms that are rarely met in atmospheric data sets. As a result, the actual coverage probability may differ considerably from the target level.

In contrast, the computer-intensive subsampling methodology yields CIs of asymptotically correct coverage under very weak assumptions. The problem is that atmospheric time series are often prohibitively short, so that subsampling CIs may undercover (note, however, that “classical” alternatives to them are often unavailable).

The construction of subsampling CIs involves the rate of convergence for the estimator of the parameter. In the talk, it will be demonstrated how the actual coverage of subsampling CIs can be made close to the target by replacing the asymptotic (known or unknown) rate of convergence with that found via simulations with approximating models, with examples of ABL time series analysis.

This work is supported by the National Science Foundation Grant AGS-1050588.