Duals of random vectors and processes with applications to prediction problems with missing values
详细信息    查看全文
文摘
Important results in prediction theory dealing with missing values have been obtained traditionally using difficult techniques based on duality in Hilbert spaces of analytic functions [Nakazi, T., 1984. Two problems in prediction theory. Studia Math. 78, 7–14; Miamee, A.G., Pourahmadi, M., 1988. Best approximations in and prediction problems of Szegö, Kolmogorov, Yaglom, and Nakazi. J. London Math. Soc. 38, 133–145]. We obtain and unify these results using a simple finite-dimensional duality lemma which is essentially an abstraction of a regression property of a multivariate normal random vector (Rao, 1973) or its inverse covariance matrix. The approach reveals the roles of duality and biorthogonality of random vectors in dealing with infinite-dimensional and difficult prediction problems. A novelty of this approach is its reliance on the explicit representation of the prediction error in terms of the data rather than the predictor itself as in the traditional techniques. In particular, we find a new and explicit formula for the dual of the semi-finite process {Xt;t≤n} for a fixed n, which does not seem to be possible using the existing techniques.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址：北京市海淀区学院路29号 邮编：100083

电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700