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

      see “Freeman — Tukey”
      see “Likelihood ratio statistic
notation      see “Stochastic order” “Stochastic
$\chi^2$       see “Pearson's chi square”
Additive models      23—24; see also “Partitioning chi square” “Lancaster's
Agreement, measures of      393—400 501—502; measures
AID      see “Automatic interaction detection”
Angular transformation for binomial      367—369 491—492; “transformations variance-stabilizing”
Anomalies in data      332—337
Arcsin transformation      367—369 491—492
Association, measures of, asymptotic variances for      374 501—502
Association, measures of, for $2 \times 2$ tables      376—385
Association, measures of, for $I \times J$ tables      385—393
Association, measures of, geometry of      383—385
Association, measures of, interpretability of      374—375
Association, measures of, norming      375—376
Association, measures of, sensitivity to margins      375 392—393; measures “Correlation “u-terms”
Association, measures of, symmetry      376
Association, surface of constant      52—53
Asymptotic theory      457—530; see also “Bayes estimators”
Automatic interaction detection      360
BAN (best asymptotic normal)      58 26 349 352 518
Bayes estimators      404—410
Bayes estimators, asymptotic results for      410—416
Bayes estimators, risk function of      406—407
Bayes estimators, small sample results for      416—419 421—424
Binomial distribution      see also “Sampling distributions”
Binomial distribution, angular transformation for      332—337 367—369 491—492
Binomial distribution, asymptotic distribution of powers      478—479 488
Binomial distribution, asymptotic normality of      464—465
Binomial distribution, behavior of minimax estimators for      416—417
Binomial distribution, estimation of proportion      437
Binomial distribution, estimation of sample size      437—438
Binomial distribution, moments of      436—437
Binomial distribution, negative      316—317 339—340 452—454 500
Binomial distribution, orders of      477
Binomial distribution, variance of squared proportions      485
Binomial distribution, variance stabilization for      491—492
Birch's results for MLEs, regularity conditions for      509—5
Birch's results for MLEs, uniqueness of      69
Block-diagonal table, l8      2
Block-stairway table, l9      4 98
Block-triangular table l9      4 98
Bootstrap-Bayes estimators      see “Pseudo-Bayes estimators”
Breaking-apart      see “Rearranging data”
BSS (between-group sum of squares)      390
Capture-recapture models, general      246—254
Capture-recapture models, incomplete tables and      233 237—239 246—247
Capture-recapture models, interpreting dependencies in      230 255
Capture-recapture models, three-sample      237—245
Capture-recapture models, two-sample      231—237
Cell values      see also “Configuration” “Zero
Cell values, elementary      13 61
Cell values, nonelementary      61
Cell values, smoothing      123 401—433
Cell values, standardized residual      136—139
Cell values, sums of      61
Chains, Markov for different strata      277—279
Chains, Markov, order of      269—270
Chernoff — Pratt theory      see “Stochastic order” “Stochastic
Chi square distribution, percentage points of      527; see also “Chi square statistic”
Chi square statistic      see also “Minimum logit $\chi^2$ ” “Neyman's “Pearson's
Chi square statistic, association measures based on      330—332 385—387
Chi square statistic, asymptotic distribution, under alternative hypothesis      329—330 473—474 518
Chi square statistic, asymptotic distribution, under null hypothesis      472—473 516—218
Chi square statistic, comparing several      330—332
Closed-form estimates      see “Direct estimates”
Cochran's Q test      307—309
Cochran's test for combined tables      146—147
Cohen's measure of agreement, K      395—397
Collapsing, general definition of      47
Collapsing, general theorem for      47—48
Collapsing, illustration of      41—43
Collapsing, theorem for      3
Collapsing, two-way tables      27—28
Collapsing, way array      39—40
Combination of $2 \times 2$ tables      365—366; see also “Mantel — Haensel test” “Collapsing”
Combining categories      27—29; see also “Collapsing”
Complete data, fitting incomplete models to      111—114; see also “Incomplete arrays” “Comprehensive
Complete tables, definition of      58
Comprehensive model, definition      38 66—67
Computer programs      7
Conditional distribution      see also “Incomplete tables”
Conditional distribution, exact theory for      364—366
Conditional distribution, for Poisson variates      440—441;
Conditional tests for interaction      148 364—366
Conditional tests for marginal homogeneity      293—296 307—309
Confidence interval      see also “Variance asymptotic”
Confidence interval for measures of association      374 380 382
Confidence interval, asymptotic for cell probability, p      478
Confidence interval, use of asymptotic variances for      499—500
Configuration of same order, degrees of freedom      119—122
Configuration, correspondence of, with u-terms      66
Configuration, definition of      61
Configuration, empty cells in      90
Connectivity      see “Separability”
Constructing tables      25—26
Contingency tables      57
Continuous variables      360
Contrasts      see “Linear contrasts”
Convergence in distribution      463—465 467—475
Convergence in distribution and       478—479
Convergence in distribution and       474
Convergence in distribution and probability      477—479
Convergence in probability      465—467
Convergence of moments      484—486
Correlation coefficient, association measures based on      380—385
Correlation coefficient, chi square and      382
Correlation coefficient, partial, related to collapsing      41
Correlation coefficient, related to cross product      14—15
Correlation coefficient, variance stabilization of      500—50
Cramer's measure of association, V      386—387
Cross-product ratio as loglinear contrast      15 26—27
Cross-product ratio related to correlation coefficient      15
Cross-product ratio related to u-terms      17—18
Cross-product ratio, association measures based on      377—380 393
Cross-product ratio, asymptotic variance of      377 494—497
Cross-product ratio, definition of      13
Cross-product ratio, functions of      379 601
Cross-product ratio, interpretation of      14—15
Cross-product ratio, properties of      14 377
Cross-validation of models      319—320
Cyclic descent, method of      see “Fitting iterative proportional”
D-association      see “Separability”
D-separability      see “Separability”
Degrees of freedom for closed-form models      121—122
Degrees of freedom for complete tables      25 35 66 114—122
Degrees of freedom for marginal homogeneity      287 294 307
Degrees of freedom for quasi-independence      187—188
Degrees of freedom for quasi-loglinear models      216—220
Degrees of freedom for quasi-symmetry      287 303
Degrees of freedom for symmetry      283 301—302
Degrees of freedom, adjusting, for empty cells      115—119
Delta method for binomial distribution      481—482
Delta method for calculating asymptotic distributions      486—502
Delta method for capture-recapture problem      249—250
Delta method, multivariate theorem      492—497
Delta method, one-dimensional theorem      487—490
Deming — Stephan procedure      see “Fitting iterative
Direct estimates for multiway incomplete tables      217 221—223 248
Direct estimates for quasi-independence      192—201
Direct estimates in three or four dimensions      74—75
Direct estimates, difference between models with      129—130
Direct estimates, equivalence to iterative      74 201—202
Direct estimates, partitioning for models with      170—171
Direct estimates, rules for detecting      76—77
Direct estimates, theorems for detecting      78—82
Dirichlet distribution      405—406
Disagreement      398—399; see also “Agreement”
Distributions      see Sampling distributions

e, approximating      460—462
Empirical-Bayes      see “Pseudo-Bayes”
Empty cells      see “Zero entries”
Entropy, maximum, theorem relating to linear models      346; see also “Information theory”
Error, prediction, measures of reduction in      387—389
Estimability of parameters in incomplete table      219—220
Estimability, compared with connectedness      2l5
Estimation see      “BAN” “Bayes “Information “Maximum “Minimum methods” “Minimum
Exact theory for $2 \times 2$ tables      364—365
Exact theory for combined tables      365—366
Exact theory, practicability of      366
Exponential distribution as limit of long waiting times      467—468
Exponential distribution, distribution of minimum      477—478
Fitting, iterative proportional      see also “Maximum likelihood estimates”
Fitting, iterative proportional for asymptotic variances      250—251 253—254
Fitting, iterative proportional for MLEs      83
Fitting, iterative proportional for quasi-symmetry      289
Fitting, iterative proportional in three dimensions      84—85
Fitting, iterative proportional, classical usage      97—102 337 392
Fitting, iterative proportional, convergence of      85—87 94—95 289
Fitting, iterative proportional, general algorithm      91—97
Fitting, iterative proportional, incomplete tables      188—192 217
Fitting, iterative proportional, initial estimates      92—95
Fitting, iterative proportional, properties of      83
Fitting, iterative proportional, stopping rules      95—96
Four-fold table ( $2 \times 2$ table), definition of      11—12
Four-fold table ( $2 \times 2$ table), descriptive parameters ofl      13—14
Four-fold table ( $2 \times 2$ table), geometry of      49—55 383—385
Freeman — Tukey, chi square      130 137 513—516
Freeman — Tukey, transformation for binomial      367—368 492
Freeman — Tukey, transformation for Poisson      137 492
Freeman — Tukey, transformation, residuals for      130 137—140 334—337
Frequency of frequencies      337—342; see also “Sampling distributions”
Geometry of Bayes estimators      408—410
Geometry of measures for $2 \times 2$ tables      49—55 383—385
Gini's definition of variation      389—390
Goodness-of-fit      see also “Chi square” “Likelihood “Neyman's “Pearson's
Goodness-of-fit for sampling distributions      3l5—317
Goodness-of-fit of internal cells      l36—141
Goodness-of-fit when model is false      329—332
Goodness-of-fit, asymptotic distribution of test statistics for      513—529
Goodness-of-fit, asymptotic equivalence of 3 statistics      513—514
Goodness-of-fit, fitting and testing for      317—324
Goodness-of-fit, multinomial general theory of      507—508
Goodness-of-fit, too good a fit      324—329
Hansen frequencies, asymptotic distribution of      489
Hierarchy of models      320—324
Hierarchy principle      33 38 67—68
Homeogeneity of proportions      347
Homeogeneity, marginal      54—55 282
Homeogeneity, test for      293—296 306—309
Homogeneous Markov chain      262
Hypergeometric distribution      see also “Exact theory”
Hypergeometric distribution, multivariate      450—452
Hypergeometric distribution, univariate      488—450
Incomplete arrays for subsets of complete arrays      111 206—210 225—228
Incomplete arrays, multiway      210—225
Incomplete arrays, square tables and      283 290
Incomplete arrays, triangular      31
Incomplete arrays, two-way      178—206
Independence as lack of association      374—380
Independence in rectangular array      28—29
Independence in three-way array      38
Independence, quasi      178—182 287—293
Independence, surface of      51
Indirect estimates      see “Fitting iterative “Partitioning
Information theory, minimum discrimination information (MDI)      344—347
Information theory, model generation      345—346
Information theory, modified MDI (MMDI)      295—296 347
Interaction      see also “u-terms”
Interaction, assessing magnitude of      146—155
Interaction, test for      146—155 364—366
Irregular arrays      31 48;
Isolates      l93
Iterative proportional fitting      83—102 188—191
Iterative scaling      see “Iterative proportional fitting”
Jackknifing      3l9
K, sum of Dirichlet parameters      401—402 405—408 420—426; K”
Kullback — Liebler distance      345; see also “Information theory” “Likelihood
Lambda as measure of association      388—389
Lambda as weight for Dirichlet prior      405—406 419—426 429—433
Latent structure analysis      344
Least squares, weighted      352—357
Likelihood ratio statistic,       125—130
Likelihood ratio statistic, for direct models      129—130 158—160
Likelihood ratio statistic, for incomplete tables      191
Likelihood ratio statistic, for indirect models, bounds for      160—161
Likelihood ratio statistic, for symmetry      283
Likelihood ratio statistic, , asymptotic distribution of      513—5 6
Likelihood ratio statistic, , calculus for partitioning      169—175
Likelihood ratio statistic, , compared with Pearson's chi-square      125—126
Likelihood ratio statistic, , conditional breakdown of      120 127
Likelihood ratio statistic, , conditional test for marginal homogeneity      293—294 307
Likelihood ratio statistic, , definition of      58
Likelihood ratio statistic, , structural breakdown of      127—130
Linear contrast      see also “Log-linear model” “u-terms”
Linear contrast, asymptotic variance of      494—497
Linear contrast, interpretations of      15 16 26—27 181 211—222
Linear models      see “Additive models”
Log-linear model      see also “Linear contrast” “Cross “Direct
Log-linear model for $2 \times 2 \times 2$ table      32—33
Log-linear model for $2 \times 2$ table      16—17 79
Log-linear model for $I \times J \times K$ table      35—41
Log-linear model for $I \times J \times K$ table, interpretation of      37 39
Log-linear model for $I \times J$ table      24—26 179
Log-linear model with terms of uniform order      119—121 156—158
Log-linear model, general      42—47
Log-linear model, general, interpretation of      45—47
Log-linear model, random effects models      371
Logistic response function      see also “Logit model”
Logistic response function, multivariate      360
Logistic response function, univariate      357—360
Logit model for $2 \times J$ table      30
Logit model, alternatives to      367—371
Logit model, continuous variable      358
Logit model, definition of      22—23
Logit model, discrete variable      357 361
Logit model, minimum c-hi square for      355—357
Logit model, mixed variable      358
Loglinear contrasts      see “Linear contrast”
Loops, closed      76
Mantel — Haenszel test      133 147—148 151
Marginal homogeneity      see “Homogeneity”
margins      see “Cell values” “Configuration”
Margins, lines of constant      53
Margins, measures insensitive to      392—393
Markov models for cross classified states      273—279
Markov models for different strata      277—279
Markov models, assessing order of      269—270
Markov models, assessing order of, for aggregate data      260 261
Markov models, higher order      267—270
Markov models, single sequence transitions of      270 273
Markov models, time-homogeneity      261—267 269
Maximum entropy      345—346; see also “Information theory”
Maximum likelihood estimates (MLEs)      see also “Fitting Iterative proportional” “Birch's “Direct
Maximum likelihood estimates (MLEs) for marginal homogeneity      294—295 306
Maximum likelihood estimates (MLEs) for Markov chain transition probabilities      Maximum likelihood estimates (MLEs) 262—263 267—268
Maximum likelihood estimates (MLEs) for quasi-symmetry      289 306—319
Maximum likelihood estimates (MLEs) for symmetry      28 330—302
Maximum likelihood estimates (MLEs), advantages of      58
Maximum likelihood estimates (MLEs), asymptotic behavior of      509 513
Maximum likelihood estimates (MLEs), conditional for closed populations      231 238
Maximum likelihood estimates (MLEs), existence of, for incomplete tables      186 216
Maximum likelihood estimates (MLEs), expansion of, for multinorniat      511—513
Maximum likelihood estimates (MLEs), methods of obtaining      71 83
Maximum likelihood estimates (MLEs), relative precision of      313—315
Maximum likelihood estimates (MLEs), suitability for likelihood ratio statistic      125—126
Maximum likelihood estimates (MLEs), uniqueness of in incomplete tables      185
Maximum likelihood estimates (MLEs), when model is incorrect      513
McNemar test      258 285

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