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Wolter K.M. Introduction to Variance Estimation
Wolter K.M.  Introduction to Variance Estimation







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: Introduction to Variance Estimation

: Wolter K.M.

:

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.

The book provides instruction on the methods that are vital to data-driven decision making in business, government, and academe. It will appeal to survey statisticians and other scientists engaged in the planning and conduct of survey research, and to those analyzing survey data and charged with extracting compelling information from such data. It will appeal to graduate students and university faculty who are focused on the development of new theory and methods and on the evaluation of alternative methods. Software developers concerned with creating the computer tools necessary to enable sound decision-making will find it essential.

Prerequisites include knowledge of the theory and methods of mathematical statistics and graduate coursework in survey statistics. Practical experience with real surveys is a plus and may be traded off against a portion of the requirement for graduate coursework.

This second edition reflects shifts in the theory and practice of sample surveys that have occurred since the content of the first edition solidified in the early 1980s. Additional replication type methods appeared during this period and have featured prominently in journal publications. Reflecting these developments, the second edition now includes a new major chapter on the bootstrap method of variance estimation. This edition also includes extensive new material on Taylor series methods, especially as they apply to newer methods of analysis such as logistic regression or the generalized regression estimator. An introductory section on survey weighting has been added. Sections on Hadamard matrices and computer software have been substantially scaled back. Fresh material on these topics is now readily available on the Internet or from commercial sources.

Kirk Wolter is a Senior Fellow at NORC, Director of the Center for Excellency in Survey Research, and Professor in the Department of Statistics, University of Chicago. He is a Fellow of the American Statistical Association and a Member of the International Statistical Institute. He is a past president of the International Association of Survey Statisticians and a past chair of the Survey Research Methods Section of the American Statistical Association. During the last 35 years, he has participated in the planning, execution, and analysis of large-scale complex surveys and has provided instruction in survey statistics both in America and around the world.


: en

: /

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ed2k: ed2k stats

: 2nd edition

: 2006

: 447

: 02.07.2008

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$\delta$-method      see Taylor series
AAPOR      see American Association for Public Opinion Research
Accuracy      34 162 170 280 355356
Accuracy, of variance estimate      3 354355 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 115116 146 354 367
Balanced half-sample method, alternate ascending order      126
Balanced half-sample method, asymptotic theory      25 217
Balanced half-sample method, for $n_h = 2$      180 214 373
Balanced half-sample method, for multistage sampling      27 33 46 48 88 113 117 123 210213 221 250 427428
Balanced half-sample method, for nonlinear estimators      2526 50 85 116121 142 169170 214215
Balanced half-sample method, for srs wr      165166 208 307 379
Balanced half-sample method, for without replacement sampling      11 16 46 56 60 83 116 19 121122 166
Balanced half-sample method, nearly equal sum      126
Balanced half-sample method, partial balancing      123 125 127128 138 140 365
Balanced half-sample method, semiascending order      126
Balanced half-sample method, transformations for      63 363 384387
Balanced repeated replication      see Balanced half-sample method
Base weights      264
BHS      see Balanced half-sample method
boot      see Bootstrap
Bootstrap      194217
Bootstrap estimator of variance      197 200 203 205206 208209 211 213217 220 380382
Bootstrap replicate      195 201202 204 207 211212 214217
Bootstrap sample      195211
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      190191
Case weights      see Weights
Certainty stratum      8788 240
CES      see Consumer Expenditure Survey
Characteristic of interest      78 18 290 321322 382 402 417
Clusters      see primary sampling unit
Collapsed stratum estimator      5057 97 127128 146
Collapsed stratum estimator, alternatives to      54
Commodity Transportation Survey      102105
Complementary half sample      115
Complex sample survey      24 21 25 60 179 221 231 354 369370 388 410
Components of variance      48 54 146 355 409
Composite estimator      91 235 237 239
Confidence interval      2425 32 107 217 294 298299 308 315 320 322 346347 351358 362364 388389 391 393
Consumer Expenditure Survey      9299 241 359360 391
Controlled selection      55 93 97 143 146 279
Convergence      332333
Convergence, in distribution      333
Convergence, in probability      333
Correlation coefficient      3 22 116 119 151 156 226 270271 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 273274 278279 320 356
Customary variance estimators      see Standard variance estimators
Design effect      275 277 280 288 290295 297
Distribution function      9 152153 194 382383
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      2425 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      199899 253
ECLS-K      see Early Childhood Longitudinal
ECLS-K, Study-Kindergarten Class of      199899
Economic Censuses      321
Estimator      16 819 2130 3274 8186 8891 9497 103104 107111 113125 127131 137142 144 146 148 151154 156 158184 187 190221 226 229232 234241 244 247253 257278 289293 298309 313317 335 337 345346 352 403 407408
Estimator, difference of ratios      116 140 173 244
Estimator, Horvitz Thompson      10 12 19 46 50 8586 89 103 121 140 144 168169 204 209 236237 249 260 273274 299 335 337 345346 352 403 407408
Estimator, linear      1618 23 25 36 4041 8486
Estimator, nonlinear      16 25 50 8586 116
Estimator, of variance      10
Estimator, ratio      2 6 8 1718 25 3134 55 57 66 7273 84 116 119120 127 179 193 210 220 264
Estimator, Taylor series estimator of variance      237 247
Excess observations      33 3840
Expectation      6 9 2324 35 37 42
Finite population      6 18 22 25 43 46 56 62 73 120
Flexibility of variance estimators      354
Fractional imputation      429431
Full orthogonal balance      112 120 122
Galois fields      137
Generalized regression estimator      261 263
Generalized variance functions (GVF)      6 272290
Generalized variance functions (GVF), alternative functions      275
Generalized variance functions (GVF), applied to quantitative characteristics      273
Generalized variance functions (GVF), for $\pi$ ps sampling      168169 181
Generalized variance functions (GVF), for nonlinear estimators      169170
Generalized variance functions (GVF), for srs wor      166167 171172 199
Generalized variance functions (GVF), for srs wr      163166 195
Generalized variance functions (GVF), generalized      159160
Generalized variance functions (GVF), in multistage sampling      210211 213
Generalized variance functions (GVF), in presence of nonresponse      184 187189 193
Generalized variance functions (GVF), in stratified sampling      172181
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      152153 163 166168 170172 174 182 191
Generalized variance functions (GVF), transformation for      63
Geometric mean      246247
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 112113 367368
Health Examination Survey      138 143
Hot-deck imputation      418420 422 424425 427
Ideal bootstrap estimator      195 211 213 215 220 381
Imputation variance      416 423425
Inclusion probability      7 43 8182 87 89 9495 103 122 144 168 204 249 257
Interpenetrating samples      see Random groups
Interval estimates      see Confidence interval
Jackknife method      107 151193
Jackknife method, ANOVA decomposition      156157
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 $\pi$ ps sampling      168169 181
Jackknife method, for nonlinear estimators      169170
Jackknife method, for srs wor      166167 171172 199
Jackknife method, for srs wr      163166 195
Jackknife method, generalized      159160
Jackknife method, in multistage sampling      210211 213
Jackknife method, in presence of nonresponse      184 187189 193
Jackknife method, in stratified sampling      172181
Jackknife method, number of groups for      162
Jackknife method, pseudovalue      152153 163 166168 170172 174 182 191
Jackknife method, transformation for      63
kurtosis      5873
Liapounov      373
Linearization      see Taylor series method
Logistic regression      216 265266
Mean imputation      418 420 422 429
Mean square error      3 203233 238 250 304 320 322 345 354 392 417
Measurement error      5 24 398404 406 409
Measurement error, correlated component      402404 406 409
Measurement error, effect on sample mean      418 420 427
Measurement error, effect on variance estimator      396397 402 404
Measurement error, for $\pi$ ps sampling      48 209
Measurement error, model for      152 274 199 332 369
Measurement error, random groups for      404
Measurement error, response variance      399 400 402403 406 408409
Measurement error, sample copy      402
Measurement error, total variance      404405
Measurement process      2225 35
Median      161 187 321322
Mirror Match variant      202
Monte Carlo bootstrap      215
MSE      see Mean square error
Multilevel analysis      269 271
Multiple imputation      425430
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      8788
Noncertainty stratum, noninformative      7
Nonresponse      2 5 19 22 24 81 97 138 144 148 184 187189 191 193 221 249250 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      227228
Ordinary least squares regression      216 271
PARAMETER      274 277280 303305 354 356357 363 365 370371 375 382 385386 388 398 420
Pivotal statistic      376378 380
Population      2 6 8 340 347
Poststratification      2 20 24 148 184 200 257258
Poststratification-adjusted weights      20
Pps wr      see Probability proportional to size with replacement sampling
PRECISION      1 5761 107 125127 162
Precision, coefficient of variation (CV) criteria      5758 61 90
Precision, confidence interval criteria      55
Prediction theory approach      9
Primary sampling unit (PSU)      12 27 33 50 5455 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      2122 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 4041 80 8485 116 169170 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      6364 6667 195 288 333
Recipient      295 419 430
Regression      22 50 53 56 116 119 156 172173 216219 249250
Regression coefficient      3 8 116 119 156 172 245a 249250 253 255 265267 271 357 370
Regression coefficient, Taylor series estimate of variance      246
Replicate weights      41 45 81 138 184185 187188 216217 225 366 423 431
Replication      107
Rescaling variant      200 206 208
Response error      see Measurement error
Retail Trade Survey      8691 235 241
RG      see Random group method
RG estimator      360
Sample design      5 95 185 241 357 360 364365 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 9394 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      35 317318
Size of population      7
SMSA (Standard Metropolitan Statistical Area)      93
Software for variance calculations      410
Software for variance calculations, benchmark data sets      413415
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      172181; 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 298308
Systematic sampling (sys), equal probability      27 102 144 298
Systematic sampling (sys), equal probability, alternative estimators of variance      115 117 250254 298299
Systematic sampling (sys), equal probability, empirical comparison of variance estimators      127 320 339
Systematic sampling (sys), equal probability, expected bias of variance estimators      259261 308309
Systematic sampling (sys), equal probability, expected MSE of variance estimators      259 304 315
Systematic sampling (sys), equal probability, multiple-start sampling      255258 307308
Systematic sampling (sys), equal probability, recommendations regarding variance estimation      282283 356 384
Systematic sampling (sys), equal probability, superpopulation models for      259265 308 315 322 332
Systematic sampling (sys), equal probability, variance of      250
Systematic sampling (sys), unequal probability      105 283305 332333 335 337
Systematic sampling (sys), unequal probability, alternative estimators of variance      287290
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      284286 374
Systematic sampling (sys), unequal probability, empirical comparison of variance estimators      291302
Systematic sampling (sys), unequal probability, intraclass correlation      270271 274 277 280 298
Systematic sampling (sys), unequal probability, recommendations about variance estimators      304305 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 226374
Taylor series method, asymptotic theory      353364
Taylor series method, basic theorem      398
Taylor series method, convergence of      232233
Taylor series method, second-order approximation      36 233
Taylor series method, transformations for      370379
Taylor series method, variance approximation      224 226
Taylor series method, variance estimator      11 47 227231
Taylor series method, variance estimator, easy computational algorithm      234 253
Taylor series method, variance estimator, for products and ratios      228229
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      155156 158 375
Ultimate cluster method      33 83;
Unbiased estimators of variance      see Standard variance estimators
Weights      1820 38 41 45 81 92 9497 117 122 138 184 185 187188 212 291 297 412
Yates Grundy estimator of variance      46 49 206
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