Hardcover ISBN:  9780821803714 
Product Code:  MMONO/162 
234 pp 
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Electronic ISBN:  9781470445775 
Product Code:  MMONO/162.E 
234 pp 
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Book DetailsTranslations of Mathematical MonographsVolume: 162; 1997MSC: Primary 62;
For nonparametric statistics, the last half of this century was the time when rankbased methods originated, were vigorously developed, reached maturity, and received wide recognition. The rankbased 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 signedbased approach is based on the assumption that random errors take positive or negative values with equal probabilities. Under this assumption, the sign procedures are distributionfree. 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, signbased 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.ReadershipGraduate students, research mathematicians, statisticians, and data analysts interested in statistics.

Table of Contents

Chapters

Introduction

Part I

Chapter 1. Signbased analysis of oneparameter linear regression

Chapter 2. Sign tests

Chapter 3. Sign estimators

Chapter 4. Testing linear hypotheses

Part II

Chapter 5. Least squares and least absolute deviations procedures in the simplest autoregressive model

Chapter 6. Signbased analysis of oneparameter autoregression

Chapter 7. Signbased analysis of the multiparameter autoregression


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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


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For nonparametric statistics, the last half of this century was the time when rankbased methods originated, were vigorously developed, reached maturity, and received wide recognition. The rankbased 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 signedbased approach is based on the assumption that random errors take positive or negative values with equal probabilities. Under this assumption, the sign procedures are distributionfree. 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, signbased 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.
Graduate students, research mathematicians, statisticians, and data analysts interested in statistics.

Chapters

Introduction

Part I

Chapter 1. Signbased analysis of oneparameter linear regression

Chapter 2. Sign tests

Chapter 3. Sign estimators

Chapter 4. Testing linear hypotheses

Part II

Chapter 5. Least squares and least absolute deviations procedures in the simplest autoregressive model

Chapter 6. Signbased analysis of oneparameter autoregression

Chapter 7. Signbased analysis of the multiparameter autoregression

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