Contributions to a General Asymptotic Statistical Theory: 13 (Lecture Notes in Statistics, 13) - Softcover

Pfanzagl, J.

Softcover

ISBN 10: 0387907769 ISBN 13: 9780387907765

Publisher: Springer, 1982

Synopsis

The aso theory developed in Chapters 8 - 12 presumes that the tan­ gent cones are linear spaces. In the present chapter we collect a few natural examples where the tangent cone fails to be a linear space. These examples are to remind the reader that an extension of the theo­ ry to convex tangent cones is wanted. Since the results are not needed in the rest of the book, we are more generous ab out regularity condi­ tions. The common feature of the examples is the following: Given a pre­ order (i.e., a reflexive and transitive order relation) on a family of p-measures, and a subfamily i of order equivalent p-measures, the fa­ mily ~ consists of p-measures comparable with the elements of i. This usually leads to a (convex) tangent cone 1f only p-measures larger (or smaller) than those in i are considered, or to a tangent co ne con­ sisting of a convex cone and its reflexion about 0 if both smaller and larger p-measures are allowed. For partial orders (i.e., antisymmetric pre-orders), ireduces to a single p-measure. we do not assume the p-measures in ~ to be pairwise comparable.

Edition details

• Publisher: Springer
• Publication date: 1982
• Language: English
• ISBN 10: 0387907769
• ISBN 13: 9780387907765
• Binding: Paperback
• Number of pages: 315