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Wolter K.M. — Introduction to Variance Estimation
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Íàçâàíèå: Introduction to Variance EstimationÀâòîð: Wolter K.M. Àííîòàöèÿ: We live in the information age. Statistical surveys are used every day to determine or evaluate public policy and to make important business decisions. Correct methods for computing the precision of the survey data and for making inferences to the target population are absolutely essential to sound decision making. Now in its second edition, Introduction to Variance Estimation has for more than twenty years provided the definitive account of the theory and methods for correct precision calculations and inference, including examples of modern, complex surveys in which the methods have been used successfully.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Èçäàíèå: 2nd editionÃîä èçäàíèÿ: 2006Êîëè÷åñòâî ñòðàíèö: 447Äîáàâëåíà â êàòàëîã: 02.07.2008Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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see “Taylor series” AAPOR see “American Association for Public Opinion Research” Accuracy 3—4 162 170 280 355—356 Accuracy, of variance estimate 3 354—355 365 American Association for Public Opinion Research 19 American Statistical Association 410 ASA see “American Statistical Association” B&B see “Baccalaureate and Beyond Longitudinal Study” Baccalaureate and Beyond Longitudinal Study 290 294 Balanced half-sample method 113 115—116 146 354 367 Balanced half-sample method, alternate ascending order 126 Balanced half-sample method, asymptotic theory 25 217 Balanced half-sample method, for 180 214 373 Balanced half-sample method, for multistage sampling 27 33 46 48 88 113 117 123 210—213 221 250 427—428 Balanced half-sample method, for nonlinear estimators 25—26 50 85 116—121 142 169—170 214—215 Balanced half-sample method, for srs wr 165—166 208 307 379 Balanced half-sample method, for without replacement sampling 11 16 46 56 60 83 116 19 121—122 166 Balanced half-sample method, nearly equal sum 126 Balanced half-sample method, partial balancing 123 125 127—128 138 140 365 Balanced half-sample method, semiascending order 126 Balanced half-sample method, transformations for 63 363 384—387 Balanced repeated replication see “Balanced half-sample method” Base weights 264 BHS see “Balanced half-sample method” boot see “Bootstrap” Bootstrap 194—217 Bootstrap estimator of variance 197 200 203 205—206 208—209 211 213—217 220 380—382 Bootstrap replicate 195 201—202 204 207 211—212 214—217 Bootstrap sample 195—211 Bootstrap, BWO variant 201 Bootstrap, BWR variant 201 Bootstrap, Correction factor variant 200 206 208 Bootstrap, Mirror — Match variant 202 Bootstrap, rescaling variant 200 206 208 BRR see “Balanced repeated replication” Capture-recapture estimator 190—191 Case weights see “Weights” Certainty stratum 87—88 240 CES see “Consumer Expenditure Survey” Characteristic of interest 7—8 18 290 321—322 382 402 417 Clusters see “”primary sampling unit Collapsed stratum estimator 50—57 97 127—128 146 Collapsed stratum estimator, alternatives to 54 Commodity Transportation Survey 102—105 Complementary half sample 115 Complex sample survey 2—4 21 25 60 179 221 231 354 369—370 388 410 Components of variance 48 54 146 355 409 Composite estimator 91 235 237 239 Confidence interval 24—25 32 107 217 294 298—299 308 315 320 322 346—347 351—358 362—364 388—389 391 393 Consumer Expenditure Survey 92—99 241 359—360 391 Controlled selection 55 93 97 143 146 279 Convergence 332—333 Convergence, in distribution 333 Convergence, in probability 333 Correlation coefficient 3 22 116 119 151 156 226 270—271 300 302 313 340 357 359 384 389 397 Correlation coefficient, asymptotic theory for 389 Cost of variance estimators 3 302 338 cps see “Current Population Survey” CTS see “Commodity Transportation Survey” Current Population Survey (CPS) 55 93 107 143 189 258 273—274 278—279 320 356 Customary variance estimators see “Standard variance estimators” Design effect 275 277 280 288 290—295 297 Distribution function 9 152—153 194 382—383 Distribution function, Bernoulli 62 Distribution function, beta 67 Distribution function, discrete uniform 63 Distribution function, exponential 72 Distribution function, gamma 70 Distribution function, logarithmic series 65 Distribution function, mixed uniform 72 Distribution function, normal 24—25 69 73 139 Distribution function, poisson 64 Distribution function, standard Weibull 71 Distribution function, triangular 68 Distribution function, uniform 63 66 72 Donor 83 419 427 430 Double sampling 2 15 22 33 Double sampling designs 217 Dual-system estimator see “Capture recapture estimator” Early Childhood Longitudinal Study-Kindergarten Class of 1998—99 253 ECLS-K see “Early Childhood Longitudinal” ECLS-K, Study-Kindergarten Class of 1998—99 Economic Censuses 321 Estimator 1—6 8—19 21—30 32—74 81—86 88—91 94—97 103—104 107—111 113—125 127—131 137—142 144 146 148 151—154 156 158—184 187 190—221 226 229—232 234—241 244 247—253 257—278 289—293 298—309 313—317 335 337 345—346 352 403 407—408 Estimator, difference of ratios 116 140 173 244 Estimator, Horvitz — Thompson 10 12 19 46 50 85—86 89 103 121 140 144 168—169 204 209 236—237 249 260 273—274 299 335 337 345—346 352 403 407—408 Estimator, linear 16—18 23 25 36 40—41 84—86 Estimator, nonlinear 16 25 50 85—86 116 Estimator, of variance 10 Estimator, ratio 2 6 8 17—18 25 31—34 55 57 66 72—73 84 116 119—120 127 179 193 210 220 264 Estimator, Taylor series estimator of variance 237 247 Excess observations 33 38—40 Expectation 6 9 23—24 35 37 42 Finite population 6 18 22 25 43 46 56 62 73 120 Flexibility of variance estimators 354 Fractional imputation 429—431 Full orthogonal balance 112 120 122 Galois fields 137 Generalized regression estimator 261 263 Generalized variance functions (GVF) 6 272—290 Generalized variance functions (GVF), alternative functions 275 Generalized variance functions (GVF), applied to quantitative characteristics 273 Generalized variance functions (GVF), for 168—169 181 Generalized variance functions (GVF), for nonlinear estimators 169—170 Generalized variance functions (GVF), for srs wor 166—167 171—172 199 Generalized variance functions (GVF), for srs wr 163—166 195 Generalized variance functions (GVF), generalized 159—160 Generalized variance functions (GVF), in multistage sampling 210—211 213 Generalized variance functions (GVF), in presence of nonresponse 184 187—189 193 Generalized variance functions (GVF), in stratified sampling 172—181 Generalized variance functions (GVF), justification for 274 277 Generalized variance functions (GVF), log-log plot 280 Generalized variance functions (GVF), model fitting 288 Generalized variance functions (GVF), negative estimates 279 Generalized variance functions (GVF), number of groups for 162 Generalized variance functions (GVF), pseudovalue 152—153 163 166—168 170—172 174 182 191 Generalized variance functions (GVF), transformation for 63 Geometric mean 246—247 Geometric mean, estimation of variance for 246 Greco-Latin square 132 GREG estimator see “Generalized regression estimator” GVF see “Generalized variance functions” Hadamard matrices 6 112—113 367—368 Health Examination Survey 138 143 Hot-deck imputation 418—420 422 424—425 427 Ideal bootstrap estimator 195 211 213 215 220 381 Imputation variance 416 423—425 Inclusion probability 7 43 81—82 87 89 94—95 103 122 144 168 204 249 257 Interpenetrating samples see “Random groups” Interval estimates see “Confidence interval” Jackknife method 107 151—193 Jackknife method, ANOVA decomposition 156—157 Jackknife method, asymptotic properties 117 154 162 183 232 355 370 389 Jackknife method, basic estimator 5 89 144 302 347 Jackknife method, bias reduction 151 158 176 Jackknife method, for 168—169 181 Jackknife method, for nonlinear estimators 169—170 Jackknife method, for srs wor 166—167 171—172 199 Jackknife method, for srs wr 163—166 195 Jackknife method, generalized 159—160 Jackknife method, in multistage sampling 210—211 213 Jackknife method, in presence of nonresponse 184 187—189 193 Jackknife method, in stratified sampling 172—181 Jackknife method, number of groups for 162 Jackknife method, pseudovalue 152—153 163 166—168 170—172 174 182 191 Jackknife method, transformation for 63 kurtosis 58—73 Liapounov 373 Linearization see “Taylor series method” Logistic regression 216 265—266 Mean imputation 418 420 422 429 Mean square error 3 203—233 238 250 304 320 322 345 354 392 417 Measurement error 5 24 398—404 406 409 Measurement error, correlated component 402—404 406 409 Measurement error, effect on sample mean 418 420 427 Measurement error, effect on variance estimator 396—397 402 404 Measurement error, for 48 209 Measurement error, model for 152 274 199 332 369 Measurement error, random groups for 404 Measurement error, response variance 399 400 402—403 406 408—409 Measurement error, sample copy 402 Measurement error, total variance 404—405 Measurement process 22—25 35 Median 161 187 321—322 Mirror — Match variant 202 Monte Carlo bootstrap 215 MSE see “Mean square error” Multilevel analysis 269 271 Multiple imputation 425—430 Multiply-adjusted imputation 427 Multipurpose surveys 61 Multistage sampling 27 33 46 48 88 113 117 123 210 221 250 427 National Crime Survey 247 National Longitudinal Survey of Youth 83 185 221 National Postsecondary Student Aid Study 294 Newton — Raphson iterations 216 NLSY97 see “National Longitudinal Survey of Youth” Noncertainty stratum 87—88 Noncertainty stratum, noninformative 7 Nonresponse 2 5 19 22 24 81 97 138 144 148 184 187—189 191 193 221 249—250 257 264 279 Nonresponse-adjusted weights 19 Nonsampling errors 6 Nonself-representing PSU 93 96 144 279 NSR PSU see “Nonself-representing PSU” Order in probability 227—228 Ordinary least squares regression 216 271 PARAMETER 274 277—280 303—305 354 356—357 363 365 370—371 375 382 385—386 388 398 420 Pivotal statistic 376—378 380 Population 2 6 8 340 347 Poststratification 2 20 24 148 184 200 257—258 Poststratification-adjusted weights 20 Pps wr see “Probability proportional to size with replacement sampling” PRECISION 1 57—61 107 125—127 162 Precision, coefficient of variation (CV) criteria 57—58 61 90 Precision, confidence interval criteria 55 Prediction theory approach 9 Primary sampling unit (PSU) 12 27 33 50 54—55 87 93 113 Probability measure 7 Probability per draw 10 Probability proportional to size with replacement sampling 10 165 Pseudoreplication see “Balanced half-sample method” Pseudovalues see “Jackknife method” PSU see “Primary sampling unit” Quasirange see “Range” Quenouille's estimator see “Jackknife method” Raking-ratio estimator (RRE estimator) 264 Random group method 21—22 27 44 73 83 88 97 103 107 195 Random group method, asymptotic theory 217 370 374 380 Random group method, basic rules for 81 89 94 108 113 131 Random group method, for multistage sampling 88 123 Random group method, general estimation procedure 33 Random group method, independent case 170 Random group method, linear estimators 16 17 25 36 40—41 80 84—85 116 169—170 174 196 217 Random group method, nonindependent case 73 83 170 Random group method, number of 38 60 83 355 365 Random group method, transformations for 384 RANGE 63—64 66—67 195 288 333 Recipient 295 419 430 Regression 22 50 53 56 116 119 156 172—173 216—219 249—250 Regression coefficient 3 8 116 119 156 172 245a 249—250 253 255 265—267 271 357 370 Regression coefficient, Taylor series estimate of variance 246 Replicate weights 41 45 81 138 184—185 187—188 216—217 225 366 423 431 Replication 107 Rescaling variant 200 206 208 Response error see “Measurement error” Retail Trade Survey 86—91 235 241 RG see “Random group method” RG estimator 360 Sample design 5 95 185 241 357 360 364—365 370 Sample median 161 Sample size 7 SASS see “Schools and Staffing Survey” Schools and Staffing Survey 288 Second order 7 Self-representing PSU 33 93—94 146 Simple random sampling with replacement (srs wr) 113 163 196 Simple random sampling without replacement (srs wor) 2 11 17 Simplicity of variance estimators 3—5 317—318 Size of population 7 SMSA (Standard Metropolitan Statistical Area) 93 Software for variance calculations 410 Software for variance calculations, benchmark data sets 413—415 Software for variance calculations, characteristics of 415 Software for variance calculations, environment for 415 SR PSU see “Self-representing PSU” Srs wor see “Simple random sampling without replacement” Srs wr see “Simple random sampling with replacement” Standard Metropolitan Statistical Areas see “SMSA” Standard variance estimators 5 Stratified sampling 172—181; see also “Collapsed stratum estimator” Student's t distribution 377 385 426 Survey Research Methods Section 410 Survey weights 18 213 215 255 270 Sys see “Systematic sampling” Systematic sampling (sys) 6 27 33 41 48 144 185 298—308 Systematic sampling (sys), equal probability 27 102 144 298 Systematic sampling (sys), equal probability, alternative estimators of variance 115 117 250—254 298—299 Systematic sampling (sys), equal probability, empirical comparison of variance estimators 127 320 339 Systematic sampling (sys), equal probability, expected bias of variance estimators 259—261 308—309 Systematic sampling (sys), equal probability, expected MSE of variance estimators 259 304 315 Systematic sampling (sys), equal probability, multiple-start sampling 255—258 307—308 Systematic sampling (sys), equal probability, recommendations regarding variance estimation 282—283 356 384 Systematic sampling (sys), equal probability, superpopulation models for 259—265 308 315 322 332 Systematic sampling (sys), equal probability, variance of 250 Systematic sampling (sys), unequal probability 105 283—305 332—333 335 337 Systematic sampling (sys), unequal probability, alternative estimators of variance 287—290 Systematic sampling (sys), unequal probability, approximate fpc 169 288 338 Systematic sampling (sys), unequal probability, confidence interval coverage probabilities 302 354 363 Systematic sampling (sys), unequal probability, description of 284—286 374 Systematic sampling (sys), unequal probability, empirical comparison of variance estimators 291—302 Systematic sampling (sys), unequal probability, intraclass correlation 270—271 274 277 280 298 Systematic sampling (sys), unequal probability, recommendations about variance estimators 304—305 355 Systematic sampling (sys), unequal probability, relative bias of variance estimators 300 356 Systematic sampling (sys), unequal probability, relative MSE of variance estimators 301 356 Taylor series method 50 226—374 Taylor series method, asymptotic theory 353—364 Taylor series method, basic theorem 398 Taylor series method, convergence of 232—233 Taylor series method, second-order approximation 36 233 Taylor series method, transformations for 370—379 Taylor series method, variance approximation 224 226 Taylor series method, variance estimator 11 47 227—231 Taylor series method, variance estimator, easy computational algorithm 234 253 Taylor series method, variance estimator, for products and ratios 228—229 Taylor series method, variance estimator, with other variance methods 354 Textbook variance estimators see “Standard variance estimators” Thickened range see “Range” Time series models 313 Timeliness of variance estimators 3; see also “Cost of variance estimators” Total variance 6; see also “Measurement error” Transformations 384 Transformations, Bartlett's family of 386 Transformations, Box — Cox family of 388 Transformations, Z-transformation 389 U-statistics 155—156 158 375 Ultimate cluster method 33 83; Unbiased estimators of variance see “Standard variance estimators” Weights 18—20 38 41 45 81 92 94—97 117 122 138 184 185 187—188 212 291 297 412 Yates — Grundy estimator of variance 46 49 206
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