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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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536 461 464 461 462 507 464 492 462 465 Acceptance 215 Action space 17 Adaptation 388 Algorithm 102 127 Algorithm, BISECTION 127 210 Algorithm, coordinate ascent 129 Algorithm, EM 133 Algorithm, Newton — Raphson 102 132 189 210 Algorithm, Newton — Raphson for GLM 413 Algorithm, proportional fitting 157 alternative 215 217 Analysis of variance (Anova) 367 Analysis of variance (ANOVA), table 379 antisymmetric 207 209 Asymptotic distribution of quadratic forms 510 Asymptotic efficiency 331 Asymptotic efficiency of Bayes estimate 342 Asymptotic efficiency of MLE 331 386 Asymptotic equivalence of MLE and Bayes estimate 342 Asymptotic normality 311 Asymptotic normality of estimate 300 Asymptotic normality of M-estimate, estimating equation estimate 330 Asymptotic normality of minimum contrast estimate 327 Asymptotic normality of MLE 331 386 Asymptotic normality of posterior 339 391 Asymptotic normality of sample correlation 319 Asymptotic order in probability notation 516 Asymptotic relative efficiency 357 Autoregressive model 11 292 Bayes credible bound 251 Bayes credible interval 252 Bayes credible region 251 Bayes credible region, asymptotic 344 Bayes estimate 162 Bayes estimate, Bernoulli trials 166 Bayes estimate, equivalence 168 Bayes estimate, Gaussian model 163 Bayes estimate, linear 167 Bayes risk 162 Bayes rule 27 162 Bayes' rule 445 479 482 Bayes' theorem 14 Bayesian models 12 Bayesian prediction interval 254 Behrens — Fisher problem 264 Bernoulli trials 447 Bernstein — von Mises theorem 339 Bernstein's inequality 469 Bernstein's inequality, binomial case 519 Berry — Esseen bound 299 Berry — Esseen theorem 471 Beta distribution 488 Beta distribution as prior for Bernoulli trials 15 Beta distribution, Moments 526 beta function 488 Bias 20 176 Bias, sample variance 78 Binomial distribution 447 461 Bioequivalence trials 198 Bivariate log normal distribution 535 Bivariate normal distribution 497 Bivariate normal distribution, cumulants 506 Bivariate normal distribution, geometry 532 Bivariate normal distribution, nondegenerate 499 Bivariate normal model 266 Cauchy distribution 526 Cauchy — Schwartz inequality 458 Cauchy — Schwarz inequality 39 Cauchy — Schwarz inequality, generalized 521 Center of a population distribution 71 Central limit theorem 470 Central Limit Theorem, Multivariate 510 Chain rule 517 Change of variable formula 452 Characteristic function 505 Chebychev bound 346 Chebychev's inequality 299 469 Chi-square distribution 491 Chi-square distribution, noncentral 530 Chi-square test 402 Chi-squared distribution 488 Classification, Bayes rule 165 Coefficient of determination 37 Coefficient of skewness 457 Collinearity 69 90 Comparison 247 Complete families of tests 232 Compound experiment 446 Concave function 518 Conditional distribution 478 Conditional distribution for bivariate normal case 501 Conditional distribution for multivariate normal case 509 Conditional expectation 483 Confidence band, quantiles, simultaneous 284 Confidence bound 23 234 235 Confidence bound, mean, nonparametric 241 Confidence bound, uniformly most accurate 248 Confidence interval 24 234 235 Confidence interval, Bernoulli trials, approximate 237 Confidence interval, Bernoulli trials, exact 244 Confidence interval, location parameter, nonparametric 286 Confidence interval, median, nonparametric 282 Confidence interval, one-sample Student t 235 Confidence interval, quantile, nonparametric 284 Confidence interval, shift parameter, nonparametric 287 Confidence interval, two-sample Student t 263 Confidence interval, unbiased 283 Confidence level 235 Confidence rectangle, Gaussian model 240 Confidence region 233 239 Confidence region, distribution function 240 Confidence regions, Gaussian linear model 383 Conjugate normal mixture distributions 92 Consistency 301 Consistency of estimate 300 301 Consistency of minimum contrast estimates 304 Consistency of MLE 305 347 Consistency of posterior 338 Consistency of test 333 Consistency, uniform 301 Contingency tables 403 Contrast function 99 Control observation 4 Convergence in 536 Convergence in law, distribution 466 Convergence in law, in distribution for vectors 511 Convergence in probability 466 Convergence in probability for vectors 511 Convergence of random variables 466 Convergence of sample quantile 536 Convex function 518 Convex support 122 Convexity 518 Correlation 267 458 Correlation, inequality 458 Correlation, multiple 40 Correlation, ratio 82 Covariance 458 Covariance of random vectors 504 Covariate 10 Covariate, stochastic 387 419 Cramer — Rao lower bound 181 Cramer — von Mises statistic 271 Critical region 23 215 Critical value 216 217 Cumulant 460 Cumulant generating function for random vector 505 Cumulant in normal distribution 460 Cumulant, generating function 460 Curved exponential family 125 Curved exponential family, existence of MLE 125 de Moivre — Laplace theorem 470 Decision rule 19 Decision rule, admissible 31 Decision rule, Bayes 27 161 162 Decision rule, inadmissible 31 Decision rule, minimax 28 170 171 Decision rule, randomized 28 Decision rule, unbiased 78 Decision theory 16 Delta method 306 Delta method for distributions 311 Delta method for moments 306 density 456 Density function 449 Density, conditional 482 Design 366 Design, matrix 366 Design, matrix, random 387 Design, values 366 Deviance 414 Deviance, decomposition 414 Dirichlet distribution 74 198 202 Distribution function (d.f.) 450 Distribution of quadratic form 533 Dominated Convergence Theorem 514 Double exponential distribution 526 Duality between confidence regions and tests 241 Duality theorem 243 Dynkin, Lehmann, Scheffe's theorem 86 Edgeworth approximations 317 Eigenvalues 520 Empirical distribution 104 Empirical distribution function 8 139 Empirical distribution function, bivariate 139 Entropy maximum 91 Error 3 Error, autoregressive 11 Estimate 99 Estimate, consistent 301 Estimate, empirical substitution 139 Estimate, estimating equation 100 Estimate, frequency plug-in 103 Estimate, Hodges — Lehmann 149 Estimate, least squares 100 Estimate, maximum likelihood 114 Estimate, method of moments 101 Estimate, minimum contrast 99 Estimate, plug-in 104 Estimate, squared error, Bayes 162 Estimate, unbiased 176 Estimating equation estimate, asymptotic normality 384 Estimation 16 Events 442 Events, independent 445 Expectation 454 455 Expectation, conditional 479 Exponential distribution 464 Exponential family 49 Exponential family, conjugate prior 62 Exponential family, convexity 61 Exponential family, curved 57 Exponential family, identifiability 60 Exponential family, log concavity 61 Exponential family, MLE 121 Exponential family, moment generating function 59 Exponential family, multiparameter 53 Exponential family, multiparameter, canonical 54 Exponential family, one-parameter 49 Exponential family, one-parameter, canonical 52 Exponential family, rank of 60 Exponential family, submodel 56 Exponential family, supermodel 58 Exponential family, UMVU estimate 186 Extension Principle 102 104 F distribution 491 F distribution, moments 530 F distribution, noncentral 531 F statistic 376 Factorization theorem 43 Fisher consistent 158 Fisher information 180 Fisher information, matrix 185 Fisher's discriminant function 226 Fisher's genetic linkage model 405 Fisher's method of scoring 434 Fitted value 372 Fixed design 387 Frechet differentiable 516 Frequency function 449 Frequency function, conditional 477 Frequency plug-in principle 103 Gamma distribution 488 Gamma distribution, Moments 526 Gamma function 488 Gamma model, MLE 124 129 130 Gauss — Marakov linear model 418 Gauss — Markov assumptions 108 Gauss — Markov theorem 418 Gaussian linear model 366 Gaussian linear model, canonical form 368 Gaussian linear model, confidence intervals 381 Gaussian linear model, confidence regions 383 Gaussian linear model, estimation in 369 Gaussian linear model, identifiability 371 Gaussian linear model, likelihood ratio statistic 374 Gaussian linear model, MLE 371 Gaussian linear model, testing 378 Gaussian linear model, UMVU estimate 371 Gaussian model, Bayes estimate 163 Gaussian model, existence of MLE 123 Gaussian model, mixture 134 Gaussian two-sample model 261 Generalised linear models (GLM) 411 Geometric distribution 72 87 GLM 412 GLM, estimate, asymptotic distributions 415 GLM, Gaussian 435 GLM, likelihood ratio test 414 GLM, likelihood ratio, asymptotic distribution 415 GLM, Poisson 435 Goodness-of-fit test 220 223 Gross error models 190 Hammersley's theorem 513 Hardy — Weinberg proportions 103 403 Hardy — Weinberg proportions, chi-square test 405 Hardy — Weinberg proportions, MLE 118 124 Hardy — Weinberg proportions, UMVU estimate 183 Hat matrix 372 Hazard rates 69 70 Heavy tails 208 hessian 386 Hierarchical Bayesian normal model 92 Hierarchical binomial-beta model 93 Hodges — Lehmann estimate 207 Hodges's example 332 Hoeffding bound 299 346 Hoeffding's inequality 519 Hoelder's inequality 518 Horvitz — Thompson estimate 178
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