Fienberg S., Holland P.W., Bishop Y.M. — Discrete Multivariate Analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Fienberg S., Holland P.W., Bishop Y.M. — Discrete Multivariate Analysis

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Название: Discrete Multivariate Analysis

Авторы: Fienberg S., Holland P.W., Bishop Y.M.

Аннотация:

The scientist searching for structure in large systems of data finds inspiration in his own discipline, support from modern computing, and guidance from statistical models. Because large sets of data are likely to be complicated, and because so many approaches suggest themselves, a codification of techniques of analysis, regarded as attractive paths rather than as straitjackets, offers the scientist valuable directions to try. The literature on discrete multivariate analysis, although extensive, is widely scattered. This book brings that literature together in an organized way.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 568

Добавлена в каталог: 14.04.2008

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Предметный указатель

MDI      see “Information theory”
mgf      see “Moment generating function”
Minimax estimates      407
Minimum distance measure      see also “Pearson's chi square” “Neyman's “Minimum
Minimum distance measure, asymptotic variance of      518—519
Minimum distance measure, methods      504—505
Minimum logit $\chi^2$       355—357
MLE      see “Maximum likelihood estimates”
MMDI      see “Information theory”
Model      see also “Log-linear model” “Additive
Model, selection of      155 168
Model, simplicity in building a      312—313
Moment generating function, to show convergence      469; see also “Sampling distribution”
Moments      see “Binomial distribution moments “Hypergeometric “Multinomial “Poisson
Moments, limits of      485
Moments, methods of      505 507
Moments, order of      485 486
Multinomial distribution, asymptotic normality of      469—472
Multinomial distribution, asymptotic variance of loglinear contrasts for      494—497
Multinomial distribution, estimation for      504—505
Multinomial distribution, formal stochastic structure for      480—481
Multinomial distribution, general theory for estimating and testing with a      502—508
Multinomial distribution, goodness-of-fit tests      507—508
Multinomial distribution, negative multinomial      454—456
Multinomial distribution, product multinomial      63 70—71
Multinomial distribution, sampling distribution      63 441—446
Multinomial distribution, variance of log-linear contrasts      494—497
Multiplicative models      225—228 320—324;
Multivariate normal distribution, asymptotic distribution for multinomial      469—472
Multivariate normal distribution, estimating the mean of      403
Nested models      see also “Likelihood ratio statistic
Nested models, difference in       524—526
Neyman's chi square, minimizing      349—350
Neyman's chi square, with linear constraints      351—352
Neyman's chi square, with linear constraints, equivalence to weighted least squares      352—354
Noninteractive cell      181—182 193—194
Normal approximations to the binomial      464—465
Norming measures of association      375—376
Notation for models, dimension-free      61—62; see also “O notation”
O,o notation, Chernoff — Pratt      479—480 481
O,o notation, conventions in use of      459—460
O,o notation, definitions      458—459 460
O,o notation, generalized for stochastic sequences      475—484
O,o notation, related to order of moments      485—486
Occurrence in probability      482—484
Outliers      140—141
P      see “Pearson's measures of association”
Panel studies      257—260 265—267
Parameters      see “u-terms”
Partial association models, degrees of freedom for      121—122
Partial association models, fitting      161—165
Partitioning chi square      524—526
Partitioning chi square, calculus of Goodman      169—175
Partitioning chi square, Lancaster's method      361—364
Partitioning chi square, likelihood ratio statistic      524—526
Pdf (probability density function)      63
Pearson's chi square      see also “Chi square distribution”
Pearson's chi square, asymptotic distribution of      472—474
Pearson's chi square, asymptotic relation to other statistics      513—516
Pearson's chi square, compared with       124—125
Pearson's chi square, correction for continuity      124 258
Pearson's chi square, definition of      57
Pearson's chi square, incomplete tables      191
Pearson's chi square, large samples and      329—332
Pearson's chi square, limiting distribution of under alternative      329—332 518
Pearson's chi square, limiting distribution of under null model      516—518
Pearson's chi square, limiting distribution of, for complex cases      520—522
Pearson's chi square, minimizing      348—349
Pearson's chi square, noncentral distribution      473—474 518
Pearson's measures of association, $\Phi^2$       330 385—387
Pearson's measures of association, P      382—383 385—387
Percentage points, for $\chi$ distribution      527—529
Poisson distribution      see also “Frequency of frequencies” “Hansen “Maximum “Sampling
Poisson distribution, asymptotic distribution of powers of mean      489—490
Poisson distribution, relationship to multinomial      440—441 446—448
Poisson distribution, sampling distribution      62 185—186 438—441 446—448
Poisson distribution, truncated variates      503—504 506 607 521—522 523—524
Poisson distribution, variance-stabilizing transform for      492
Population-size estimation      229—256
Pratt, occurrence in probability      482—484; see also “Stochastic sequence” “Notation dimension-free”
PRE (proportional reduction in error)      387—389
PRECISION      313—315; see also “Variance”
Probit transformation      367
Propagation of errors      see “Delta method”
Pseudo-Bayes estimators      408—410 419—423
Pseudo-Bayes estimators, asymptotic results for      410—416
Pseudo-Bayes estimators, small sample results for      416—419
PV (predictive value)      21—22
q      see “Association measures “Cochran's “Yule's
Quasi-independence      see “Independence”
Quasi-loglinear      210—212
Quasi-perfect mobility      206—208
Quasi-symmetry      see “Symmetry”
R $ho(\rho)$ measuring association      381—385
Rates, adjusting for multiple variables      123 133—136
Rates, direct standardization      131—132
Rates, generic form      133—136
Rates, indirect standardization      132
Rates, standard mortality ratio      132 135
Rearranging data, breaking apart an $I \times I$ table      207—209
Rearranging data, fitting by stages      107—108
Rearranging data, in $2 \times 2$ table      15—16
Rearranging data, partitioning      105—107
Rearranging data, relabeling      102—105

Regularity conditions      see “Birch's results for MLEs”
Relatives, high order      34
Risk      see also “Cross-product ratio”
Risk for comparing Bayesian estimators      406—408
Risk, expected squared error      313—335
Risk, ratios, limiting      414—416
Risk, relative      15
Sampling design, constraints on models      36
Sampling design, stratified      29—30
Sampling distribution      62—64 185 212; “Hypergeometric “Multinomial “Poisson
Sampling distribution, effect on model selection      70—71
Sampling models, search for      315—317
Saturated models      9
Scoring categorical variables      360
Search procedures      see “Stepwise model selection”
Sensitivity      20—21 48
Separability in many dimensions      212—216
Separability, dealing with      184—187
Separability, in $I \times J$ tables      182—183
Separability, semi-      194
Simplicity in model building      312—315
Smoothed counts      see “Cell values smoothing”
SMR (Standard Mortality Ratio)      see “Rates standard
Sparse multinomials      410—413
Specificity      20—22 48
Square tables      281—309 320—324 339—342 347
Standard deviation and stochastic order      476—477
Standardization      see “Fitting iterative classical “Rates”
Stationarity, of transition probabilities      261—267 269
Stepwise model selection      165—167
Stochastic order      see also “Stochastic sequence”
Stochastic order of exponential variables      477—478
Stochastic order, Chernoff — Pratt theory for      479—484
Stochastic order, definition of      475—476
Stochastic order, methods for determining      476—477
Stochastic orders of moments      485—486
Stochastic sequence      see also “Stochastic order”
Stochastic sequence, Chernoff — Pratt theory for      479—480
Stochastic sequence, convergence of      463—475
Stochastic sequence, determining order of      476—478
Stochastic sequence, formal structure of      480—482
Structural models, definition of      9—10
Structural models, uses of      11
Sufficient statistics      64—67
Sufficient statistics for three-dimensional models      66
Sufficient statistics, general derivation of      68—69
Sufficient statistics, minimal set of      66
Sufficient statistics, minimal set of, and direct estimates      78
Summary statistics      see “Association measures of” “Chi “Frequency of “Rates” ”Sufficient
Suppressing parameters      332—337
Symmetry in association measures      376
Symmetry in square tables      258 282—286 299—306 347—348
Symmetry, exact      260
Symmetry, quasi-      286—292 303 296
Symmetry, relative      260
Synergism      see “Worcester model”
t      see “Tsehuprow's measure of association”
Taylor expansion      460—461
Testing      see also “Interaction” “Partitioning
Testing and fitting      317—324
Testing, simplifying structure before      150
Testing, use of asymptotic variances for      498—499
Tetrahedron, of reference      50
Transformations, variance-stabilizing      366—371 491—492; “Arcsine “Logit “Freeman “Probit
Transition probabilities      262—269
Transition probabilities, single sequence      270—273
tree structures      360
triangular arrays      see “Incomplete arrays”
Trinomial distribution, for risk of pseudo-Bayesian estimators      417—419
Tschuprow's measure of association, T      385—387
TSS (total sum of squares)      390
U as collection of u-terms      62
U as measure of association      389—392
u-terms      see also “Log-linear model” “Linear
u-terms, definition      17 18
u-terms, generalized notation      61—62
u-terms, interpretation of      29—30 32—34
u-terms, relationship to cross-product ratios      17—18
u-terms, standardized estimates of      141 146 156
u-terms, variance of      494—497
Unsaturated models      9
V, Cramer's measure of association      386—387
Variance      see also “Delta method”
Variance for capture-recapture problem      233 240—242 248—254
Variance for distance measures      518—519
Variance, asymptotic      498—499
Variance, asymptotic for confidence intervals      499—500
Variance, asymptotic for hypothesis testing      488—499
Variance, methods for computing      248—251
Variance, stabilizing transformations      491—492 500—501
Variation, measures of      389—393
Waiting times      467—468
Worcester model      111
WSS (within-group sum of squares)      390
Y      see “Association” “Yule”
Yule's Q as measure of association      378—380 501
Yule's Y as measure of colligation      378—380
Zero entries      see also “Configuration”
Zero entries, deviations in cells with      140
Zero entries, diagonals with, in square tables      296—299
Zero entries, invalidating model      72
Zero entries, random, defined      59 177
Zero entries, structural      31 59 93 177
Zero entries, unrepeated events in Markov chains      275—276

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