Inference and Prediction in Large Dimensions

In many instances of statistical research the data and/or parameters belong to a large, or infinite, dimensional space. In such circumstances accurate inference and statistical prediction are often problematic, requiring an alternative statistical treatment. Inference and Prediction in Large Dimensions offers a predominantly theoretical coverage of statistical prediction when such dimensional spaces are involved, and discusses numerous potential applications. The authors develop the theory of statistical prediction, non-parametric estimation by adaptive projection and kernel, with applications to tests of fit and prediction, and theory of linear processes in function spaces with applications to prediction of continuous time processes. Highlighting the latest developments in the field, this book provides a comprehensive and authoritative introduction to the topic. The text is divided into three main parts covering statistical prediction, inference by projection, and inference by kernels. The applications are demonstrated with examples from fields such as finance, medicine and psychology. Inference and Prediction in Large Dimensions is aimed at graduates and researchers in the field of statistics, and students specializing in statistical inference for stochastic processes. The many potential applications also make it ideal for applied statisticians in numerous areas, as well as mathematicians and engineers.