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Bickel P., Doksum K. — Mathematical statistics
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Название: Mathematical statisticsАвторы: Bickel P., Doksum K. Аннотация: This classic, time-honored introduction to the theory and practice of statistics modeling and inference reflects the changing focus of contemporary Statistics. Coverage begins with the more general nonparametric point of view and then looks at parametric models as submodels of the nonparametric ones which can be described smoothly by Euclidean parameters. Although some computational issues are discussed, this is very much a book on theory. It relates theory to conceptual and technical issues encountered in practice, viewing theory as suggestive for practice, not prescriptive. It shows readers how assumptions which lead to neat theory may be unrealistic in practice. Statistical Models, Goals, and Performance Criteria. Methods of Estimation. Measures of Performance, Notions of Optimality, and Construction of Optimal Procedures in Simple Situations. Testing Statistical Hypotheses: Basic Theory. Asymptotic Approximations. Multiparameter Estimation, Testing and Confidence Regions. A Review of Basic Probability Theory. More Advanced Topics in Analysis and Probability. Matrix Algebra. For anyone interested in mathematical statistics working in statistics, bio-statistics, economics, computer science, and mathematics.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2ndГод издания: 2001Количество страниц: 556Добавлена в каталог: 03.01.2014Операции: Положить на полку |
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Huber estimate 207 390 Hypergeometric distribution 3 461 Hypergeometric probability 448 Hypothesis 215 Hypothesis, composite 215 Hypothesis, null 215 Hypothesis, simple 215 Identifiable 6 Independence 445 453 Independent experiments 446 Indifference region 230 Influence function 196 Information bound 181 Information bound, asymptotic variance 327 Information Inequality 179 181 186 188 206 Integrable 455 Interquartile range (IQR) 196 Invariance, shift 77 Inverse gaussian distribution 94 IQR 196 Iterated expectation theorem 481 Jacobian 485 Jacobian, theorem 486 Jensen's inequality 518 Kolmogorov statistic 220 Kolmogorov's theorem 86 Kullback — Leibler divergence 116 Kullback — Leibler divergence and MLE 116 Kullback — Leibler loss function 169 kurtosis 279 457 Laplace distribution 374 526 Law of large numbers, weak, Bernoulli's 468 Law of large numbers, weak, Khintchin's 469 Least absolute deviation estimates 149 374 Least favorable prior distribution 170 Least squares 107 120 Least squares, weighted 107 112 Lehmann alternative 275 Level (of significance) 217 Life testing 89 Likelihood equations 117 Likelihood function 47 Likelihood ratio 48 256 Likelihood ratio statistic in Gaussian linear model 376 Likelihood ratio statistic, simple 223 Likelihood ratio test 335 Likelihood ratio, asymptotic chi-square distribution 394 395 Likelihood ratio, confidence region 257 Likelihood ratio, confidence region, asymptotic 395 Likelihood ratio, logistic regression 410 Likelihood ratio, test 256 Likelihood ratio, test, bivariate normal 266 Likelihood ratio, test, Gaussian one-sample model 257 Likelihood ratio, test, Gaussian two-sample model 261 Likelihood ratio, test, one-sample scale 291 Likelihood ratio, test, two-sample scale 293 Linear model, Gaussian 366 Linear model, non-Gaussian 389 Linear model, stochastic covariates 419 Linear model, stochastic covariates, Gaussian 387 Linear model, stochastic covariates, heteroscedastic 421 Linear regression model 109 Link function 412 Link function, canonical 412 Location parameter 209 463 Location-scale parameter family 463 Location-scale regression, existence of MLE 127 Log linear model 412 Logistic distribution 57 132 Logistic distribution, likelihood equations 154 Logistic distribution, neural nets 151 Logistic distribution, Newton — Raphson 132 Logistic linear regression model 408 Logistic regression 56 90 408 Logistic transform 408 Logistic transform, empirical 409 logit 90 408 Loss function 18 Loss function, 0-1 19 Loss function, absolute 18 Loss function, Euclidean 18 Loss function, Kullback — Leibler 169 202 Loss function, quadratic 18 M-estimate 330 M-estimate, asymptotic normality 384 Marginal density 452 Markov's inequality 469 Matched pair experiment 257 Maximum likelihood 114 Maximum likelihood estimate 114 see Maximum likelihood estimate (mle) 114 Mean 71 454 455 Mean absolute prediction error 80 83 Mean squared error (MSE) 20 Mean squared prediction error (MSPE) 32 Mean, sensitivity curve 192 Median 71 Median, MSE 297 Median, population 77 80 105 Median, sample 192 Median, sensitivity curve 193 Mendel's genetic model 214 Mendel's genetic model, chi-square test 403 Meta-analysis 222 Method of moments 101 Minimax estimate, Bernoulli trials 173 Minimax estimate, distribution function 202 Minimax rule 28 170 Minimax test 173 MLE 114 see MLE as projection 371 MLE, asymptotic normality, exponential family 322 MLE, Cauchy model 149 MLE, equivariance 114 144 MLE, existence 121 MLE, uniqueness 121 MLR 228 see Model 1 5 Model, AR(1) 11 Model, Cox 70 Model, Gaussian linear regression 366 Model, gross error 190 210 Model, Lehmann 69 Model, linear 10 Model, linear, Gaussian 10 Model, location, symmetric 191 Model, logistic linear 408 Model, nonparametric 6 Model, one-sample 3 366 Model, parametric 6 Model, proportional hazard 70 Model, regression 9 Model, regular 9 Model, scale 69 Model, semiparametric 6 Model, shift 4 Model, symmetric 68 Model, two-sample 4 moment 456 Moment generating function 459 Moment generating function for random vector 504 Moment of random matrix 502 Moment, central 457 Monotone likelihood ratio (MLR) 228 Monte Carlo method 219 221 298 314 MSE 20 see MSE, sample mean 21 MSE, sample variance 78 MSPE 32 see MSPE predictor 83 372 MSPE, bivariate normal 36 MSPE, multivariate normal 37 Multinomial distribution 462 Multinomial trials 55 447 462 Multinomial trials in contingency tables 403 Multinomial trials, consistent estimates 302 Multinomial trials, Dirichlet prior 198 Multinomial trials, estimation, asymptotic normality 324 Multinomial trials, Kullback — Leibler loss, Bayes estimate 202 Multinomial trials, minimax estimate 201 Multinomial trials, MLE 119 124 Multinomial trials, Pearson's chi-square test 401 Multinomial trials, UMVU estimate 187 Multiple correlation coefficient 37 Multivariate normal distribution 506 Natural parameter space 52 54 Natural sufficient statistic 54 Negative binomial distribution 87 Neural net model 151 Neyman allocation 76 Neyman — Pearson framework 23 Neyman — Pearson lemma 224 Neyman — Pearson test 165 Noncentral 376 Noncentral chi-square distribution 375 Noncentral t distribution 260 Nonnegative definite 519 Normal distribution 464 see Normal distribution, central moments 529 Normal equations 101 Normal equations, weighted least squares 113 Normalizing transformation, zero skewness 351 Observations 5 One-way layout 367 One-way layout, binomial, testing 410 One-way layout, confidence intervals 382 One-way layout, testing 378 Order statistics 527 Orthogonal 41 Orthogonal matrix 494 Orthogonality 522 p-sample problem 367 p-value 221 PARAMETER 6 Parameter, nuisance 7 Parametrization 6 Pareto density 85 Pearson's chi-square 402 Placebo 4 Plug-in principle 102 Poisson distribution 462 Poisson process 472 Poisson's theorem 472 Polya's theorem 515 Population 448 Population quantile 105 Population R-squared 37 Positive definite 519 Posterior 13 Power function 78 217 Power function, asymptotic 334 Power function, sample size 230 Prediction 16 32 Prediction error 32 Prediction error, absolute 33 Prediction error, squared 32 Prediction error, squared, weighted 84 Prediction interval 252 Prediction interval, Bayesian 254 Prediction interval, distribution-free 254 Prediction interval, Student t 253 Prediction, training set 19 Predictor 32 Predictor, linear 38 39 Principal axis theorem 519 Prior 13 Prior, conjugate 15 Prior, conjugate, binomial 15 Prior, conjugate, exponential family 62 Prior, conjugate, general model 73 Prior, conjugate, multinomial 74 Prior, conjugate, normal case 63 Prior, conjugate, Poisson 73 Prior, improper 163 Prior, Jeffrey's 203 Prior, least favorable 170 probability distribution 451 Probability, conditional 444 Probability, continuous 449 Probability, discrete 443 449 Probability, distribution 442 Probability, subjective 442 Probit model 416 Product moment 457 Product moment, central 457 Projection 41 371 Projection matrix 372 Projections on linear spaces 522 Pythagorean identity 41 377 Pythagorean identity in Hilbert space 522 Quality control 229 Quantile, population 104 Quantile, sensitivity curve 195 Random 441 Random design 387 Random effects model 167 Random experiments 441 Random variable 451 Random vector 451 Randomization 5 Randomized test 79 224 Rank 48 ranking 16 Rao score 399 Rao score, confidence region 400 Rao score, statistic 399 Rao score, statistic, asymptotic chi-square distribution 400 Rao score, test 399 Rao score, test, multinomial goodness-of-fit 402 Rao test 335 336 Rayleigh distribution 53 Regression 9 366 Regression line 502 regression toward the mean 36 Regression, confidence intervals 381 Regression, confidence regions 383 Regression, heteroscedastic 58 153 Regression, homoscedastic 58 Regression, Laplace model 149 Regression, linear 109 Regression, location-scale 57 Regression, logistic 56 Regression, Poisson 204 Regression, polynomial 146 Regression, testing 378 Regression, weighted least squares 147 Regression, weighted, linear 112 Rejection 215 Relative frequency 441 Residual 48 111 372 Residual, sum of squares 379 Response 10 366 Risk function 20 Risk function, maximum 28 Risk function, testing 22 Risk set 29 Risk set, convexity 79 Robustness 190 418 Robustness of level, asymptotic 419 Robustness of level, t-statistics 314
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