Sign-Based Methods in Linear Statistical Models (Translations of Mathematical Monographs) - Hardcover

M. V. Boldin, G. I. Simonova, And Yu. N. Tyurin

Hardcover

ISBN 10: 0821803719 ISBN 13: 9780821803714

Publisher: American Mathematical Society, 1997

Synopsis

For nonparametric statistics, the last half of this century was the time when rank-based methods originated, were vigorously developed, reached maturity, and received wide recognition. The rank-based approach in statistics consists in ranking the observed values and using only the ranks rather than the original numerical data. In fitting relationships to observed data, the ranks of residuals from the fitted dependence are used. The signed-based approach is based on the assumption that random errors take positive or negative values with equal probabilities. Under this assumption, the sign procedures are distribution-free. These procedures are robust to violations of model assumptions, for instance, to even a considerable number of gross errors in observations. In addition, sign procedures have fairly high relative asymptotic efficiency, in spite of the obvious loss of information incurred by the use of signs instead of the corresponding numerical values. In this work, sign-based methods in the framework of linear models are developed. In the first part of the book, there are linear and factor models involving independent observations. In the second part, linear models of time series, primarily autoregressive models, are considered.

About this title

Language Notes

Text: English (translation)
Original Language: Russian

Edition details

• Publisher: American Mathematical Society
• Publication date: 1997
• Language: English
• ISBN 10: 0821803719
• ISBN 13: 9780821803714
• Binding: Hardcover
• Number of pages: 234