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1981 | Buch

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Simultaneous Statistical Inference

verfasst von: Rupert G. Miller Jr.

Verlag: Springer New York

Buchreihe : Springer Series in Statistics

Enthalten in: Professional Book Archive

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Über dieses Buch

Simultaneous Statistical Inference, which was published originally in 1966 by McGraw-Hill Book Company, went out of print in 1973. Since then, it has been available from University Microfilms International in xerox form. With this new edition Springer-Verlag has republished the original edition along with my review article on multiple comparisons from the December 1977 issue of the Journal of the American Statistical Association. This review article covered developments in the field from 1966 through 1976. A few minor typographical errors in the original edition have been corrected in this new edition. A new table of critical points for the studentized maximum modulus is included in this second edition as an addendum. The original edition included the table by K. C. S. Pillai and K. V. Ramachandran, which was meager but the best available at the time. This edition contains the table published in Biometrika in 1971 by G. 1. Hahn and R. W. Hendrickson, which is far more comprehensive and therefore more useful. The typing was ably handled by Wanda Edminster for the review article and Karola Decleve for the changes for the second edition. My wife, Barbara, again cheerfully assisted in the proofreading. Fred Leone kindly granted permission from the American Statistical Association to reproduce my review article. Also, Gerald Hahn, Richard Hendrickson, and, for Biometrika, David Cox graciously granted permission to reproduce the new table of the studentized maximum modulus. The work in preparing the review article was partially supported by NIH Grant ROI GM21215.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

To whom the first thoughts on simultaneous statistical inference or multiple comparisons should be attributed is an obscure historical point which is not of prime importance to this monograph. Likely as not, it was a nonstatistician. What one can be certain of is that simultaneous inference did not burst into existence one fine morning in full, completed form, but rather evolved slowly from the treatment of special cases until the general applicability and merit of the underlying principles were recognized and molded into a general theory and philosophy.

Rupert G. Miller Jr.

Chapter 2. Normal Univariate Techniques

Abstract

This chapter contains a number of multisample and regression techniques whose distribution theory assumes an underlying normal distribution. It includes, in particular, the fundamental work of Duncan, Seheffé, and Tukey. Those techniques which are peculiar primarily to regression (e.g., prediction and discrimination) are discussed in Chapter 3, even though they are directly related, and in some instances special cases of the methods in this chapter. The nonparametric analogs of the techniques in this chapter are covered in Chapter 4.

Rupert G. Miller Jr.

Chapter 3. Regression Techniques

Abstract

The previous chapter covered the techniques available for simultaneously testing, or bracketing in confidence intervals, a set of regression coefficients. This chapter treats the other three problems often associated with regression analysis: banding the regression surface, prediction, and discrimination.

Rupert G. Miller Jr.

Chapter 4. Nonparametric Techniques

Abstract

This chapter covers those simultaneous techniques whose test statistics have a null distribution which does not depend on the form of the underlying distribution generating the sample observations. A few restrictions are usually placed on the underlying sample distribution, but they are minor in character.

Rupert G. Miller Jr.

Chapter 5. Multivariate Techniques

Abstract

A preponderance of the work on multivariate simultaneous confidence intervals and tests is contained in two articles: Roy and Bose (1953) and Dunn (1958). The remaining material appears in Roy (1954,1956), Seheffé (1956,1959), Healy (1956), and Anderson (1965). A summary of the work of Roy and Bose is given in Roy (1957).

Rupert G. Miller Jr.

Chapter 6. Miscellaneous Techniques

Abstract

This chapter groups together a variety of techniques whose discussions are too short to constitute separate chapters. For the most part the techniques are unrelated, hence the title of this chapter.

Rupert G. Miller Jr.

Erratum to: Addendum New Table of the Studentized Maximum Modulus

Abstract

In the original edition the Pillai and Ramachandran (1954) table of critical points for the studentized maximum modulus was included in Appendix B as Table III. These critical points and a few additional points computed by Dunn and Massey (1965) were the only ones readily available at the time. The need for a more comprehensive table was filled by Hahn and Hendrickson in 1971. They tabulated critical points for the multivariate t distribution with common correlation ρ = 0,.2,.4, and.5. Their Table 1 for the studentized maximum modulus (ρ = 0) is reproduced from Biometrika in this second edition as Table IIIA with the permission of the authors and the editor.

Rupert G. Miller Jr.

Backmatter

Titel: Simultaneous Statistical Inference
verfasst von: Rupert G. Miller Jr.
Verlag: Springer New York
Electronic ISBN: 978-1-4613-8122-8
Print ISBN: 978-1-4613-8124-2
DOI: https://doi.org/10.1007/978-1-4613-8122-8

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Über dieses Buch

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Chapter 2. Normal Univariate Techniques

Chapter 3. Regression Techniques

Chapter 4. Nonparametric Techniques

Chapter 5. Multivariate Techniques

Chapter 6. Miscellaneous Techniques

Erratum to: Addendum New Table of the Studentized Maximum Modulus

Backmatter