Confidence sets for high-dimensional empirical linear prediction (HELP) models with dependent error structure

In this paper, we provide asymptotic theory and use it to construct confidence sets for High-dimensional Empirical Linear Prediction (HELP) Models. HELP is a statistical prediction technique based on a model similar to a factor analysis model. The aim of HELP model, however, is to predict future observations, and is different from the usual factor analysis. We generalize HELP to the cases of non-iid errors, thus going beyond the standard factor analysis model. We studied an unusual asymptotic theory where the size of the covariance matrix goes to infinity. This kind of asymptotic theory is important for practical applications and leads to confidence sets with much better coverage probabilities than the ones derived from the typical asymptotic theory where the size of the covariance matrix remains fixed. Although the covariance matrix may not be estimated consistently, it is shown that the point estimates of HELP are consistent. Also, valid asymptotic confidences sets are constructed based on the inconsistently estimated covariance matrix. (C) 2002 Elsevier Science B.V. All rights reserved.