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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
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 $\mathcal{F}$ distribution      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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