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Bishop Y.M.M., Feinberg S.E., Holland P.W. Discrete Multivariate Analysis, Theory and Practice
Bishop Y.M.M., Feinberg S.E., Holland P.W.  Discrete Multivariate Analysis, Theory and Practice







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: Discrete Multivariate Analysis, Theory and Practice

: Bishop Y.M.M., Feinberg S.E., Holland P.W.

: en

: /

:

ed2k: ed2k stats

: 1975

: 593

: 25.06.2008

: | | ID
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$(FT)^2$      see Freeman Tukey
$G^2$      see Likelihood ratio statistic
$O_P$, $o_P$ notation      
see Stochastic order Stochastic
$X^2$      see Pearsons chi square
Abelson, R.P      359 531
Additive models      2324 (see also Partitioning chi square Lancasters
Agreement, measures of      393400 501502 measures
AID      see Automatic interaction detection
Aitchison, J.      370 531
Altham, P      393 403531
Anderson, T.W      260 262 265 267 274 531
Andrewartha, H.G.      234 531
Angular transformation for binomial      367369 491492 Transformations variance-stabilizing)
Anomalies in data      332337
Anscombe, F.J.      454 531
Arcsin transformation      367369 491492
Armitage, P.      400 531
Association, measures of, asymptotic variances for      374 501502
Association, measures of, for $2\times 2$ tables      376385
Association, measures of, for IxJ tables      385393
Association, measures of, geometry of      383385
Association, measures of, interpretability of      374375
Association, measures of, norming      375376
Association, measures of, sensitivity to margins      375 392393 measures Correlation u-terms)
Association, measures of, symmetry      376
Association, surface of constant      5253
Asymptotic theory      457530 (see also Bayes estimators)
Automatic interaction detection      360
Bahadur, R.R.      415
BAN (best asymptotic normal)      58 126 349 352 518
Bartlett, M.S      63 83 87 270 357 363 368 531
Bayes estimators      404410
Bayes estimators, asymptotic results for      410416
Bayes estimators, risk function of      406407
Bayes estimators, small sample results for      416419 421424
Beard, J.H.      90 537
Beck, A      230 531
Bennett, B.M.      400 531
Benson, L.      99 531
Berelson, B.      265 537
Bergerson, H.W.      340
Berkson, J.      126 347 355 358 531
Bhapkar, V.P.      284 306 352 353 531 532
Bhat.B.R      370 532
Binomial distribution, angular transformation for      332337 367369 491492
Binomial distribution, asymptotic distribution of powers      478479 488
Binomial distribution, asymptotic normality of      464465
Binomial distribution, behavior of minimax estimators for      416417
Binomial distribution, estimation of proportion      437
Binomial distribution, estimation of sample size      437438
Binomial distribution, moments of      436437
Binomial distribution, negative      316317 339340 452454 500
Binomial distribution, orders of      477
Binomial distribution, variance of squared proportions      485
Binomial distribution, variance stabilization for      491492 (see also Sampling distributions)
Birch, M.W.      3764 69 94 146 161 365 366 446 509 511 532
Birchs results for MLEs, uniqueness of      69
Birchs results for MLEs, uniqueness of, regularity conditions for      509511
Bishop, Y.M.M.      7 41 105 106 124 125 134 135 148 150 178 193 196 197 198 401 532
Black, M.M.      102 103 538
Blackwell, D.      532
Blendis, L.M      400 531
Bloch, D.      403 532
Block-diagonal table      182
Block-stairway table      194198
Block-triangular table      194198
Bock, R D.      84 142 344 360 532
Bootstrap-Bayes estimators      see Pseudo-Bayes estimators
Bortkiewicz, L.V.      325 532
Bose, RC      182 532
Bowker, A.H      283 284 532
Braungart, R G.      379 380 532
Breaking-apart      see Rearranging data
Brown, D.R      85 532
BSS (between-group sum of squares)      390
Bush, N.      182 534
Bush, R      260 262 532
Byars, J.A.      410 540
Cameron, W.R      178 532
Capture-recapture models, incomplete tables and      233 237239 246247
Capture-recapture models, incomplete tables and, general      246254
Capture-recapture models, incomplete tables and, interpreting dependencies in      230 255
Capture-recapture models, incomplete tables and, three-sample      237245
Capture-recapture models, incomplete tables and, two-sample      231237
Cassedy, J.H.      362 532
Caussinus, H.      178 284 286 287 289 294 298 532
Cell values, elementary      13 61
Cell values, nonelementary      61
Cell values, smoothing      123 401433
Cell values, standardized residual      136139
Cell values, sums of      61 (see also Configuration Zero
Chains, Markov for different strata      277279
Chains, Markov, order of      269270
Chapman, D.C.      237 532
Chase, G.R      524 532
Chatfield, C      275 532
Chen, W.Y      178 532
Chernoff Pratt theory      see Stochastic order Stochastic
Chernoff, H      475 480 523 533
Chi square distribution, percentage points of      527 (see also Chi square statistic)
Chi square statistic,      see also Minimum logit $c^2$ Neymans Pearsons
Chi square statistic, association measures based on      310332 385387
Chi square statistic, asymptotic distribution, under null hypothesis      472473 516518
Chi square statistic, asymptotic distribution, under null hypothesis, under alternative hypothesis      329330 473474 518
Chi square statistic, comparing several      330332
Closed-form estimates      see Direct estimates
Cochran, W.G.      63 146 307 366 533
Cochrans Q test      307309
Cochrans test for combined tables      146147
Cohen, J      395 396 533 534
Cohen, J.E.      152 153 213 533
Cohens measure of agreement, K      395397
Cole, N.W.      403 539
Coleman, J.S      397 533
Collapsing, general definition of      47
Collapsing, general theorem for      4748
Collapsing, illustration of      4143
Collapsing, theorem for 3-way array      3940
Collapsing, two-way tables      2728
Colton, T.      230 542
Combination of $2 \times 2$ tables      365366 (see also Mantel Haensel Collapsing)
Combining categories      2729 (see also Collapsing)
Complete data, fitting incomplete models to      111114 (see also Incomplete arrays Comprehensive
Complete tables, definition of      58
Comprehensive model, definition      38 6667
Computer programs      7
Conditional distribution for Poisson variates      440441 (see also Incomplete tables)
Conditional distribution, exact theory for      364366
Conditional tests, for interaction      148 364366
Conditional tests, for marginal homogeneity      293296 307309
Confidence interval, asymptotic for cell probability, p      478
Confidence interval, asymptotic for measures of association      374 380 382
Confidence interval, asymptotic, use of asymptotic variances for      499500 (see also Variance asymptotic)
Configuration, correspondence of, with u-terms      66
Configuration, definition of      61
Configuration, empty cells in      90
Configuration, of same order, degrees of freedom      119122
Connectivity      see Separability
Conover, J.      124 533
Constructing tables      2526
Contingency tables      57
Continuous variables      360
Contrasts      see Linear contrasts
Convergence in distribution      463465 467475
Convergence in distribution and $O_n(1)$      478479
Convergence in distribution and $O_p(1)$      474
Convergence in distribution and probability      477479
Convergence in probability      465467
Convergence of moments      484486
Cormack, R.C      229 248 533
Cornfield, J.      359 360 365 366 533 541
Correlation coefficient, association measures based on      380385
Correlation coefficient, chi square and      382
Correlation coefficient, partial, related to collapsing      41
Correlation coefficient, related to cross product      1415
Correlation coefficient, variance stabilization of      500501
Cox, D.R      1 143 358 359 360 365 368 533
Craddock, J.M      140 533
Craig, A.T.      65 536
Craig, W.      275 276 277 533
Cramer, H      348 386 393 486 533
Cramers measure of association, V      386387
Crittenden, L.B.      178 532
Cross-product ratio, as loglinear contrast      15 2627
Cross-product ratio, association measures based on      377380 393
Cross-product ratio, asymptotic variance of      377 494497
Cross-product ratio, definition of      13
Cross-product ratio, functions of      379 601
Cross-product ratio, interpretation of      1415
Cross-product ratio, properties of      14 377
Cross-product ratio, related to correlation coefficient      15
Cross-product ratio, related to u-terms      1718
Cross-validation of models      319320
Cyclic descent, method of      see Fitting iterative
D-association      see Separability
D-separability      see Separability
Darroch, J.N.      85 101 229 240 247 248 249 250 289 533
Das Gupta, P.      240 246 247 533
Das.T.      191 192 533
Davis, J.A.      373 533
Davis, P.J      411 533
Dawber, T.R      358 533
Degrees of freedom, adjusting, for empty cells      115119
Degrees of freedom, for closed-form models      121122
Degrees of freedom, for complete tables      25 35 66 114122
Degrees of freedom, for marginal homogeneity      287 294 307
Degrees of freedom, for quasi-independence      187188
Degrees of freedom, for quasi-loglinear models      216220
Degrees of freedom, for quasi-symmetry      287 303
Degrees of freedom, for symmetry      283 301302
Delta method, for binomial distribution      481482
Delta method, for calculating asymptotic distributions      486502
Delta method, for capture-recapture problem      249250
Delta method, multivariate theorem      492497
Delta method, one-dimensional theorem      487490
Deming Stephan procedure      see Fitting iterative
Deming, W.E.      84 233 234 235 247 533 540
Deutsch, K.W      178 540
Devinney, L.C      137 138 160 541
Dickey, J.M      404 533 534
Direct estimates, difference between models with      129130
Direct estimates, equivalence to iterative      74 201202
Direct estimates, for multiway incomplete tables      217221223 248
Direct estimates, for quasi-independence      192201
Direct estimates, in three or four dimensions      7475
Direct estimates, partitioning $G^2$ for models with      170171
Direct estimates, rules for detecting      7677
Direct estimates, theorems for detecting      7882
Dirichlet distribution      405406
Disagreement      398399 (see also Agreement)
Distributions      see Sampling distributions
Duncan, D.B.      359 360 541
e, approximating      460462
Eccleston, J.      215 534
Eckler, A.R      340 341 342534
Efron, B.      403 534
Einhorn, H.      360 534
Elston, R.C      182 534
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      387389
Estimability, compared with connectedness      215
Estimability, of parameters in incomplete table      219220
Estimation      see BAN Bayes Information Maximum Minimum methods Minimum
Everett, B.S.      396 534
Exact theory, for $2\times 2$ tables      364365
Exact theory, for combined tables      365366
Exact theory, practicability of      366
Exponential distribution, as limit of long waiting times      467468
Exponential distribution, distribution of minimum      477478
Feller, W.      261 428 464 469 524
Fienberg, S.E      50 52 53 54 55 85 99 164 178 186 193 196 197 198 210 221 222 224 221 229 210 234 231 404 401 402
Fienberg, S.E.      413 414 416 417 418 421 422 423 425 429 433 496 532 534 541
Finney, D.J      367 371 534
Fisher, R.A.      58 63 328 364 365 367 453 489 527 534
Fitting, iterative proportional, classical usage      97102 337 392
Fitting, iterative proportional, convergence of      8587 9495 289
Fitting, iterative proportional, for asymptotic variances      250251 253254
Fitting, iterative proportional, for MLEs      83
Fitting, iterative proportional, for quasi-symmetry      289
Fitting, iterative proportional, general algorithm      9197
Fitting, iterative proportional, in three dimensions      8485
Fitting, iterative proportional, incomplete tables      188192 217
Fitting, iterative proportional, initial estimates      9295
Fitting, iterative proportional, properties of      83
Fitting, iterative proportional, stopping rules      9596 (see also Maximum likelihood estimates)
Fleiss, J.L      1 396 400 534
Flood, C.R      140 533
Foa, U.      297 298 299 534
Four-fold table ($2\times 2$ table), definition of      1112
Four-fold table ($2\times 2$ table), descriptive parameters of      1314
Four-fold table ($2\times 2$ table), geometry of      4955 383385
Francis, W.N      331 537
Frank, M      220 221 534
Freeman Tukey, chi square      130 137 513516
Freeman Tukey, chi square, transformation for binomial      367368 492
Freeman Tukey, chi square, transformation for Poisson      137 492
Freeman Tukey, chi square, transformation, residuals for      130 137140 334337
Freeman, M.F      137 367 492 534
Frei, E      371
Freidlander, D      97 98 534
Frequency of frequencies      337342 (see also Sampling distributions)
Fryer, J.G      306 535
Gafarian, A.V      524 539
Gage, N.L      275 542
Gart, J      353 365 366 535
Gaudet, H      265 537
Geiger, H      233 535
Geometry, of Bayes estimators      408410
Geometry, of measures for $2\times 2$ tables      4955 383385
Gilbert, J.R      52 53 54 55 384 534
Gini, C      389 390 535
Ginis definition of variation      389390
Girshick, M.A      532
Glass, D.V      100 206 209 320 427 535
Goldman, A      132 535
Good, I.J      1 337 338 345 346 403 406 425 535
Goodman, L.A      84 127 137 143 146 148 166 169 177 178 182 183 190 193 196 200 201 207 209 225 226 227 228 260 262 265 266 267 270 320 322 323 353 373 374 375 376 380 387 388 389 391 393 502 531 535 536
Goodness-of-fit, asymptotic distribution of test statistics for      513529
Goodness-of-fit, asymptotic equivalence of 3 statistics      513514
Goodness-of-fit, fitting and testing for      317324
Goodness-of-fit, for sampling distributions      315317
Goodness-of-fit, multinomial general theory of      507508
Goodness-of-fit, of internal cells      136141
Goodness-of-fit, too good a fit      324329
Goodness-of-fit, when model is false      329332 (see also Chi square Likelihood Neymans Pearsons
Greenhouse, S.W      124 538
Grizzle, J.E      124 284 306 308 353 354 536
Gross, R      369 402 536
Gumbel, E.J      327 536
Haberman, S      7 64 65 70 84 85 178185 189 193 208 216 250 452 536
Haenszel, W      146 367 538
Haight, F.A      435 536
Haldane, J.B.S      442 536
Halkka, O      224 536
Halperin, M      178 538
Hansen frequencies, asymptotic distribution of      489
Hansen, E.W      489 536
Harris, J.A      183 184 204 205 536
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