## Parameter Estimation and Hypothesis Testing in Linear ModelsThe 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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### Contents

II | 3 |

IV | 4 |

VI | 5 |

VII | 6 |

VIII | 8 |

IX | 11 |

XI | 13 |

XII | 19 |

LXXIV | 146 |

LXXV | 149 |

LXXVI | 150 |

LXXVII | 152 |

LXXVIII | 153 |

LXXX | 156 |

LXXXI | 158 |

LXXXII | 161 |

XIII | 23 |

XIV | 33 |

XV | 34 |

XVI | 36 |

XVII | 40 |

XVIII | 41 |

XIX | 44 |

XX | 46 |

XXI | 48 |

XXII | 50 |

XXIII | 54 |

XXIV | 57 |

XXV | 62 |

XXVI | 64 |

XXVII | 65 |

XXVIII | 66 |

XXIX | 68 |

XXX | 71 |

XXXI | 75 |

XXXIII | 77 |

XXXIV | 78 |

XXXV | 79 |

XXXVI | 81 |

XXXVIII | 82 |

XXXIX | 83 |

XL | 86 |

XLI | 88 |

XLII | 90 |

XLIV | 92 |

XLV | 93 |

XLVII | 96 |

XLVIII | 99 |

XLIX | 106 |

L | 107 |

LI | 111 |

LII | 112 |

LIII | 114 |

LIV | 115 |

LV | 117 |

LVI | 118 |

LVII | 120 |

LVIII | 122 |

LIX | 123 |

LX | 124 |

LXI | 126 |

LXII | 128 |

LXIII | 130 |

LXIV | 132 |

LXV | 133 |

LXVI | 135 |

LXVII | 136 |

LXIX | 137 |

LXX | 140 |

LXXII | 141 |

LXXIII | 143 |

LXXXIII | 162 |

LXXXIV | 165 |

LXXXV | 170 |

LXXXVI | 177 |

LXXXVII | 178 |

LXXXVIII | 181 |

LXXXIX | 183 |

XC | 185 |

XCI | 193 |

XCII | 197 |

XCIII | 200 |

XCIV | 204 |

XCV | 207 |

XCVI | 208 |

XCVII | 210 |

XCVIII | 212 |

XCIX | 214 |

C | 216 |

CI | 220 |

CII | 221 |

CIII | 225 |

CIV | 229 |

CV | 233 |

CVI | 237 |

CVII | 238 |

CVIII | 240 |

CIX | 241 |

CX | 246 |

CXI | 250 |

CXII | 253 |

CXIII | 255 |

CXIV | 258 |

CXV | 261 |

CXVI | 263 |

CXVII | 265 |

CXVIII | 268 |

CXIX | 271 |

CXX | 272 |

CXXI | 274 |

CXXII | 276 |

CXXIII | 279 |

CXXIV | 283 |

CXXV | 286 |

CXXVI | 288 |

CXXVII | 294 |

CXXVIII | 296 |

CXXIX | 301 |

CXXX | 302 |

CXXXI | 304 |

CXXXII | 306 |

CXXXIII | 307 |

311 | |

327 | |

### Other editions - View all

Parameter Estimation and Hypothesis Testing in Linear Models Karl-Rudolf Koch No preview available - 2012 |

Parameter Estimation and Hypothesis Testing in Linear Models Karl-Rudolf Koch No preview available - 1988 |

### Common terms and phrases

arbitrary best linear unbiased called computed constraints coordinates covariance components covariance matrix cumulative distribution function defined denotes density function derived determined eigenvalues elementary events error estimable function estimator a2 example expected values F-distribution factor full column rank full rank Gauss-Markoff model Gaussian elimination given Hence hypothesis testing idempotent identical introduced KOCH least squares leverage points linear function linear unbiased estimator m x n matrix M-estimation method of least moment generating function multivariate model n x 1 random n x 1 vector n x n non-central normal equations null hypothesis obtained orthogonal parameter estimation polynomial positive definite positive semidefinite Proof pseudoinverse quadratic form random variables Xi random vector rankA reflexive generalized inverse residuals Section solution subspace sum of squares symmetrical reflexive test for outliers test statistic transformation triangular matrix unbiased estimator unique unit weight univariate model unknown parameters variance a2 variance and covariance vector space Wishart distribution