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Sign-Based Methods in Linear Statistical Models
M. V. Boldin, G. I. Simonova, and Yu. N. Tyurin, Moscow State University, Russia
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Translations of Mathematical Monographs
1997; 234 pp; hardcover
Volume: 162
ISBN-10: 0-8218-0371-9
ISBN-13: 978-0-8218-0371-4
List Price: US$104
Member Price: US$83.20
Order Code: MMONO/162
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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.

Readership

Graduate students, research mathematicians, statisticians, and data analysts interested in statistics.

Reviews

"Presents a unified approach to fundamental statistical problems based on certain functionals of the signs of residuals. The authors designed the book for a broad spectrum of readers interested in statistical inferences ... both applied and theoretical statisticians will find the book quite interesting."

-- Mathematical Reviews

Table of Contents

  • Introduction
Part 1. Linear models of independent observations
  • Sign-based analysis of one-parameter linear regression
  • Sign tests
  • Sign estimators
  • Testing linear hypotheses
Part 2. Linear models of time series
  • Least squares and least absolute deviations procedures in the simplest autoregressive model
  • Sign-based analysis of one-parameter autoregression
  • Sign-based analysis of the multiparameter autoregression
  • Bibliography
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