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Bickel P., Doksum K. — Mathematical statistics
Bickel P., Doksum K. — Mathematical statistics

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Название: Mathematical statistics

Авторы: 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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd

Год издания: 2001

Количество страниц: 556

Добавлена в каталог: 03.01.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L_{p}$ norm      536
$\mathcal{B}(n,\theta)$, binomial distribution with parameters n and $\theta$      461
$\mathcal{E}(\lambda)$, exponential distribution with parameter $\lambda$      464
$\mathcal{H}(D,N,n)$, hypergeometric distribution with parameters D,N,n      461
$\mathcal{M}(n,\theta_{1},...,\theta_{q})$, multinomial distribution with parameters n,$\theta_{1},...,\theta_{q}$      462
$\mathcal{N}(\mu,\Sigma)$, multivariate normal distribution      507
$\mathcal{N}(\mu,\sigma^{2})$, normal distribution with mean $\mu$ and variance $\sigma^{2}$      464
$\mathcal{N}(\mu_{1},\mu_{2},\sigma^{2}_{1},\sigma^{2}_{2},\rho)$, bivariate normal distribution      492
$\mathcal{P}(\lambda)$, Poisson distribution with parameter $\lambda$      462
$\mathcal{U}(a,b)$, uniform distribution on the interval (a,b)      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 $L_{p}$ norm      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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