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Rao C.R., Toutenberg H. — Linear models: least squares and alternatives
Rao C.R., Toutenberg H. — Linear models: least squares and alternatives

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Название: Linear models: least squares and alternatives

Авторы: Rao C.R., Toutenberg H.

Аннотация:

Provides a current account of the theory and applications of linear models. Presents a unified theory of inference from linear models with minimal assumptions through least squares theory, and using alternative methods of estimation and testing based on convex loss functions and general estimating equations.


Язык: en

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 439

Добавлена в каталог: 08.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$G^2$-statistic      318
$I\times J$ contingency table      290
$R_1$-Optimal Estimators      98
$R_1(\hat{\beta}, \beta, \alpha)$      98
$R_2$-optimal estimators      102
$R_2(\hat{\beta}, \beta, \alpha)$      98
$R_3$-optimal estimators      103
$R_3(\hat{\beta}, \hat{\beta})$      98
$X_*\beta$ superiority      191
$X_*\beta$-superiority      195
$y_*$ superiority      192
a priori restrictions      72 75
ad hoc criteria      50
Adjusted coeffient of determination      51
Aitken estimator      104
Aitken least square      132
Albert’s theorem      376
Algorithm, Fisher-scoring      297
Algorithm, iterative proportional fitting (IPF)      326
Analysis of covariance — Bartlett's method      247
Analysis of variance (Anova)      44
Andrews — Pregibon statistic      228
ANOVA table      45 49
AR(1)-process      343
Association parameters      320 323
Autoregression      109
Available case analysis      242 255
Bahadur-type representation      279
Best linear unbiased estimation      27
Best linear unbiased estimator (BLUE)      104
Beta-binomial distribution      301
Biased      33
Biased linear restrictions      146
Biased stochastic restrictions      168
Binary response      300 316
Binary response variable      305
Binomial distribution      290
Bivariate, binary correlated response      344
Bivariate, regression      44
Bivariate, scatterplot      56
blue      104
Bootstrap, estimator      266
Bootstrap, sample      266
Canonical form      57
Canonical link      292
Categorical response variables      290
categorical variables      303
Cauchy — Schwarz inequality      370
Censored regression      80
Central limit theorem      310
Chain rule      295
Chebyschev’s inequality      387
Classical linear regression model      19
Classical multivariate linear regression model      17
Classical prediction      184
Cluster      300 336
Cobb — Douglas production function      7
Coding of response models      331
Coefficient of determination      47
Coefficient of determination, adjusted      51 52
Cold-deck imputation      243
Column space      25
Complete case analysis      242 254
Compound symmetric      108
Compound symmetric structure      336
Condition number      59
Conditional distribution      304
Conditional least-squares      27
Conditional model      337
Confidence ellipsoid      52 225
confidence intervals      47 52
Constant mean model      181
Constraints      320
Contemporaneously uncorrelated observations      122
Contingency table      303
Contingency table, $I\times J$      290
Contingency table, $I\times J\times 2$      322
Contingency table, three-way      322
Contingency table, two-way      303 311 319
Cook’s distance      226 269
Corrected logit      314
Corrected sum of squares      45
Correlated response      337
Correlation coefficient sample      46 47
Covariance matrix      310
Covariance matrix, asymptotic      310
Covariance matrix, estimated asymptotic      326
Cox approach      333
Cramer — Rao bound      37
Criteria for model choice      50
Cross-product ratio      306
Cross-validation      68
Decomposition of $\hat{\sigma}^2_{\Omega}$      42
Decomposition of a matrix      362
Decomposition of P      213
Decomposition singular-value      364
Deficiency in rank      30
Dependent binary variables      335
Design matrix for the main effects      331
Detection of outliers      220
Determinant of a matrix      356
Determination coefficient adjusted      55
Deviance      299
Diagnostic plots      224
Differences, test for qualitative      333
Dispersion parameter      292
Distribution, beta-binomial      301
Distribution, conditional      304
Distribution, logistic      316
Distribution, multinomial      307
Distribution, Poisson      307
Dummy coding      328
Dummy variable      44
Durbin — Watson test      56 113
Eckart — Young — Mirsky matrix approximation theorem      71
Econometric model      12
Effect coding      326 329
Efficiency of prediction ellipsoids      200
Eigenvalue      360
Eigenvector      360
Endodontic treatment      322
Ergodic      11
Error back-propagation      87
Estimate ridge      78
Estimate shrinkage      64
Estimating equations      301
Estimation of $\sigma^2$      34
Estimation, best linear unbiased      27
Estimation, minimax      72
Estimation, OLS      51
Estimation, ridge      59—61
Estimator OLS      44
Exact knowledge of a subvector      140
Exact linear restrictions      38
Exact restriction      59
Exchangeable correlation      343
Expected coverage      200
Exponential dispersion model      292
Exponential family      291
Externally Studentized residual      218
F-change      52 56
Filling in the missing values      243
First-order regression      259
Fisher-information matrix      294
Fisher-scoring algorithm      297
Fit, perfect      320
Fixed effect      119
Form, canonical      57
Form, reduced      6 12
Form, structural      6
Frobenius norm      70
Full rank factorization      365
Gauss — Markov Least Squares      131
Gee      340
Generalized esimation equations (GEE)      340
Generalized inverse      372
Generalized linear model (GLM)      291
Generalized linear models      289
Generalized linear regression model      18 97
GLM      291
GLM for binary response      313
GLSE      108
Goodness of fit      299
Goodness of fit, testing      310
Grouped data      313
Hat matrix      212
Hazard function, model for the      334
Hazard rate      332
Heteroscedasticity      109 225
Hierarchical models for three-way, contingency tables      324
Hot-deck imputation      243
Identification      15
Identity link      292
IEE      340 346
Inclusion of inequality restrictions in an ellipsoid      73
Independence      304
Independence estimating equations (IEE)      340
Independence, conditional      322
Independence, joint      322
Independence, mutual      322
Independence, testing      311
Independent multinomial sample      308
Independent single regression      18
Inequality restricted least squares      72
Inequality restrictions      72
Influential observations      217
Inspecting the residuals      222
Instrumental Variable Estimator      122
Interaction, test for quantitative      333
Internally Studentized residual      218
Intraclass correlation      111
Iterative proportional fitting (IPF)      326
Kernel of the likelihood      309
Keynes's model      13
Kolmogorov — Smirnov test      56
Kronecker product      17
LAD estimator      81
LAD estimator, asymptotic distribution      279
LAD estimator, multivariate case      280
LAD estimator, univariate case      272
Least absolute deviation, estimators      272
Leverage      212
Likelihood equations      37
Likelihood function      308
Likelihood ratio      38
Likelihood-ratio test      312 318
Linear estimators      32
Linear hypothesis      37 39
Linear minimax estimates      75
Linear regression      23
Linear trend model      182
Link      291
Link function      316
Link, canonical      292 338
Link, identity      292
Link, natural      292
Log odds      313
Logistic distribution      316
Logistic regression      313
Logistic regression and neural networks      87
Logistic regression model      313
Logit link      313
Logit models      313
Logit models for categorical data      317
Loglinear model      319
Loglinear model of independence      320
Long-term studies      242
LR test      47
M-estimate, general      281
M-estimate, univariate case      276
Mallows's $C_p$      52
Manova      271
MAR      244
Marginal distribution      303
Marginal model      337
Marginal probability      304
Masking effect      219
Matrix, decomposition of      362
Matrix, definite      365
Matrix, determinant      356
Matrix, diagonal      355
Matrix, differentiation of      384 386
Matrix, generalized inverse      372
Matrix, idempotent      371
Matrix, identity      355
Matrix, inverse of      358
Matrix, Moore — Penrose inverse      372
Matrix, nonsingular      356
Matrix, orthogonal      359
Matrix, partitioned      358
Matrix, rank of      359
Matrix, regular      356
Matrix, singular      356
Matrix, square      354
Matrix, trace of      355
Matrix, triangular      354
Maximum likelihood      344
Maximum-likelihood, estimates      308 311
Maximum-likelihood, methods      255
Maximum-likelihood, principle      36
MCAR      244
MDE      33
MDE, matrix comparison of two biased estimators      149
MDE, matrix comparison of two biased restricted estimators      156
MDE, matrix comparison of two linear biased estimators      154
MDE, matrix criterion      193
MDE, scalar      58
MDE, superiority      33
MDE-I, criterion      33 146
MDE-I, superiority      78
MDE-I, superiority of $\hat{\beta}(R)$      168 169
MDE-I, superiority of b(k)      62
MDE-II, criterion      147
MDE-II, superiority of $\hat{\beta}(R)$      170
MDE-III, criterion      147
MDEP      263
MDLUE      29
MDUE      28
Mean dispersion error (MDE)      33
Mean imputation      243
Mean shift model      235
Mean-shift outlier model      220
Measuring the gain in efficiency      167
Method by Yates      246
Minimax, estimate      75
Minimax, estimation      72
Minimax, principle      72 75
Minimax, risk      78
Missing at random (MAR)      244
Missing completely at random (MCAR)      244
Missing data      241
Missing data in the response      245
Missing indicator matrix      244
Missing values in the X-matrix      251
Missing values, filling in      243
Missing values, loss in efficiency      252
Missing values, maximum-likelihood estimates      257
Missing-data mechanisms      244
Misspecification      79
Misspecification of the dispersion matrix      106
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