Ebook: Parameter Estimation and Hypothesis Testing in Linear Models

The necessity to publish the second edition of this book arose when its third German edition had just been published. This second English edition is there­ fore a translation of the third German edition of Parameter Estimation and Hypothesis Testing in Linear Models, published in 1997. It differs from the first English edition by the addition of a new chapter on robust estimation of parameters and the deletion of the section on discriminant analysis, which has been more completely dealt with by the author in the book Bayesian In­ ference with Geodetic Applications, Springer-Verlag, Berlin Heidelberg New York, 1990. Smaller additions and deletions have been incorporated, to im­ prove the text, to point out new developments or to eliminate errors which became apparent. A few examples have been also added. I thank Springer-Verlag for publishing this second edition and for the assistance in checking the translation, although the responsibility of errors remains with the author. I also want to express my thanks to Mrs. Ingrid Wahl and to Mrs. Heidemarlen Westhiiuser who prepared the second edition. Bonn, January 1999 Karl-Rudolf Koch Preface to the First Edition This book is a translation with slight modifications and additions of the second German edition of Parameter Estimation and Hypothesis Testing in Linear Models, published in 1987.

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This textbook deals with the estimation of unknown parameters, the testing of hypotheses and the estimation of confidence intervals in linear models. The reader will find presentations of the Gauss-Markoff model, the analysis of variance, the multivariate model, the model with unknown variance and covariance components and the regression model as well as the mixed model for estimating random parameters. A chapter on the robust estimation of parameters and several examples have been added to this second edition. To make the book self-contained most of the necessary theorems of vector and matrix algebra and the probability distributions of test statistics are derived. Students of geodesy as well as of the natural sciences and engineering will find the emphasis on the geodetic application of statistical models extremely useful.

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This textbook deals with the estimation of unknown parameters, the testing of hypotheses and the estimation of confidence intervals in linear models. The reader will find presentations of the Gauss-Markoff model, the analysis of variance, the multivariate model, the model with unknown variance and covariance components and the regression model as well as the mixed model for estimating random parameters. A chapter on the robust estimation of parameters and several examples have been added to this second edition. To make the book self-contained most of the necessary theorems of vector and matrix algebra and the probability distributions of test statistics are derived. Students of geodesy as well as of the natural sciences and engineering will find the emphasis on the geodetic application of statistical models extremely useful.
Content:
Front Matter....Pages I-XIX
Introduction....Pages 1-1
Vector and Matrix Algebra....Pages 3-73
Probability Theory....Pages 75-147
Parameter Estimation in Linear Models....Pages 149-269
Hypothesis Testing, Interval Estimation and Test for Outliers....Pages 271-309
Back Matter....Pages 311-334

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This textbook deals with the estimation of unknown parameters, the testing of hypotheses and the estimation of confidence intervals in linear models. The reader will find presentations of the Gauss-Markoff model, the analysis of variance, the multivariate model, the model with unknown variance and covariance components and the regression model as well as the mixed model for estimating random parameters. A chapter on the robust estimation of parameters and several examples have been added to this second edition. To make the book self-contained most of the necessary theorems of vector and matrix algebra and the probability distributions of test statistics are derived. Students of geodesy as well as of the natural sciences and engineering will find the emphasis on the geodetic application of statistical models extremely useful.
Content:
Front Matter....Pages I-XIX
Introduction....Pages 1-1
Vector and Matrix Algebra....Pages 3-73
Probability Theory....Pages 75-147
Parameter Estimation in Linear Models....Pages 149-269
Hypothesis Testing, Interval Estimation and Test for Outliers....Pages 271-309
Back Matter....Pages 311-334
....