Essentially a form of targeted dimension reduction, an envelope is a construct for increasing efficiency in multivariate statistics without altering traditional goals, sometimes producing gains equivalent to increasing the sample size many times over. Recognizing that the data may contain unanticipated variation that is effectively immaterial to estimation, an envelope is a subspace that envelops the material variation and thereby reduces estimative variation and improves inference.
This talk is intended as an accessible introduction to envelopes in the context of multi-response linear models. The introductory discussion will be followed by relatively brief comments on recent advances and applications, including generalizations that move well beyond linear models. The presentation will include small examples for illustration. Emphasis will be placed on concepts and their potential impact on data analysis, and on some applications and issues that may be of interest in Biostatistics.