Contributions to a General Asymptotic Statistical Theory (Paperback)

J. Pfanzagl

ISBN 10: 0387907769 / ISBN 13: 9780387907765

Published by Springer-Verlag New York Inc., New York, NY, 1982

About this Item

Paperback. 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. The aso theory developed in Chapters 8 - 12 presumes that the tanA 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 theoA 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 condiA tions. The common feature of the examples is the following: Given a preA 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 faA 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 conA 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 compa Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Bibliographic Details

• Title: Contributions to a General Asymptotic Statistical Theory (Paperback)
• Publisher: Springer-Verlag New York Inc., New York, NY
• Publication Date: 1982
• Language: English
• ISBN 10: 0387907769
• ISBN 13: 9780387907765
• Binding: Paperback
• Condition: new

About this title

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.