{"product_id":"sampling-and-estimation-from-finite-populations-9780470682050","title":"Sampling and Estimation from Finite Populations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis comprehensive text takes a critical look at the modern development of the theory of survey sampling as well as the foundations of survey sampling, and explains how to put this theory into practice.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"A task for the current, and future, generation is the research and development of methods for integrating data from multiple sources by explicitly addressing the different measurement errors. Those who read this book and address its challenges will be well placed to deal with the research opportunities ahead—both foreseen and yet to be identified.\"\u003cbr\u003e—\u003cb\u003eCarl M. O'Brien, Lowestoft Laboratory, \u003ci\u003eInternational Statistical Review\u003c\/i\u003e\u003c\/b\u003e (2020) doi:10.1111\/insr.12420\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eList of Figures xiii\u003c\/p\u003e \u003cp\u003eList of Tables xvii\u003c\/p\u003e \u003cp\u003eList of Algorithms xix\u003c\/p\u003e \u003cp\u003ePreface xxi\u003c\/p\u003e \u003cp\u003ePreface to the First French Edition xxiii\u003c\/p\u003e \u003cp\u003eTable of Notations xxv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 A History of Ideas in Survey Sampling Theory \u003c\/b\u003e\u003cb\u003e1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Enumerative Statistics During the 19th Century 2\u003c\/p\u003e \u003cp\u003e1.3 Controversy on the use of Partial Data 4\u003c\/p\u003e \u003cp\u003e1.4 Development of a Survey Sampling Theory 5\u003c\/p\u003e \u003cp\u003e1.5 The US Elections of 1936 6\u003c\/p\u003e \u003cp\u003e1.6 The Statistical Theory of Survey Sampling 6\u003c\/p\u003e \u003cp\u003e1.7 Modeling the Population 8\u003c\/p\u003e \u003cp\u003e1.8 Attempt to a Synthesis 9\u003c\/p\u003e \u003cp\u003e1.9 Auxiliary Information 9\u003c\/p\u003e \u003cp\u003e1.10 Recent References and Development 10\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Population, Sample, and Estimation \u003c\/b\u003e\u003cb\u003e13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Population 13\u003c\/p\u003e \u003cp\u003e2.2 Sample 14\u003c\/p\u003e \u003cp\u003e2.3 Inclusion Probabilities 15\u003c\/p\u003e \u003cp\u003e2.4 Parameter Estimation 17\u003c\/p\u003e \u003cp\u003e2.5 Estimation of a Total 18\u003c\/p\u003e \u003cp\u003e2.6 Estimation of a Mean 19\u003c\/p\u003e \u003cp\u003e2.7 Variance of the Total Estimator 20\u003c\/p\u003e \u003cp\u003e2.8 Sampling with Replacement 22\u003c\/p\u003e \u003cp\u003eExercises 24\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Simple and Systematic Designs \u003c\/b\u003e\u003cb\u003e27\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Simple Random Sampling without Replacement with Fixed Sample Size 27\u003c\/p\u003e \u003cp\u003e3.1.1 Sampling Design and Inclusion Probabilities 27\u003c\/p\u003e \u003cp\u003e3.1.2 The Expansion Estimator and its Variance 28\u003c\/p\u003e \u003cp\u003e3.1.3 Comment on the Variance–Covariance Matrix 31\u003c\/p\u003e \u003cp\u003e3.2 Bernoulli Sampling 32\u003c\/p\u003e \u003cp\u003e3.2.1 Sampling Design and Inclusion Probabilities 32\u003c\/p\u003e \u003cp\u003e3.2.2 Estimation 34\u003c\/p\u003e \u003cp\u003e3.3 Simple Random Sampling with Replacement 36\u003c\/p\u003e \u003cp\u003e3.4 Comparison of the Designs with and Without Replacement 38\u003c\/p\u003e \u003cp\u003e3.5 Sampling with Replacement and Retaining Distinct Units 38\u003c\/p\u003e \u003cp\u003e3.5.1 Sample Size and Sampling Design 38\u003c\/p\u003e \u003cp\u003e3.5.2 Inclusion Probabilities and Estimation 41\u003c\/p\u003e \u003cp\u003e3.5.3 Comparison of the Estimators 44\u003c\/p\u003e \u003cp\u003e3.6 Inverse Sampling with Replacement 45\u003c\/p\u003e \u003cp\u003e3.7 Estimation of Other Functions of Interest 47\u003c\/p\u003e \u003cp\u003e3.7.1 Estimation of a Count or a Proportion 47\u003c\/p\u003e \u003cp\u003e3.7.2 Estimation of a Ratio 48\u003c\/p\u003e \u003cp\u003e3.8 Determination of the Sample Size 50\u003c\/p\u003e \u003cp\u003e3.9 Implementation of Simple Random Sampling Designs 51\u003c\/p\u003e \u003cp\u003e3.9.1 Objectives and Principles 51\u003c\/p\u003e \u003cp\u003e3.9.2 Bernoulli Sampling 51\u003c\/p\u003e \u003cp\u003e3.9.3 Successive Drawing of the Units 52\u003c\/p\u003e \u003cp\u003e3.9.4 Random Sorting Method 52\u003c\/p\u003e \u003cp\u003e3.9.5 Selection–Rejection Method 53\u003c\/p\u003e \u003cp\u003e3.9.6 The Reservoir Method 54\u003c\/p\u003e \u003cp\u003e3.9.7 Implementation of Simple Random Sampling with Replacement 56\u003c\/p\u003e \u003cp\u003e3.10 Systematic Sampling with Equal Probabilities 57\u003c\/p\u003e \u003cp\u003e3.11 Entropy for Simple and Systematic Designs 58\u003c\/p\u003e \u003cp\u003e3.11.1 Bernoulli Designs and Entropy 58\u003c\/p\u003e \u003cp\u003e3.11.2 Entropy and Simple Random Sampling 60\u003c\/p\u003e \u003cp\u003e3.11.3 General Remarks 61\u003c\/p\u003e \u003cp\u003eExercises 61\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Stratification \u003c\/b\u003e\u003cb\u003e65\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Population and Strata 65\u003c\/p\u003e \u003cp\u003e4.2 Sample, Inclusion Probabilities, and Estimation 66\u003c\/p\u003e \u003cp\u003e4.3 Simple Stratified Designs 68\u003c\/p\u003e \u003cp\u003e4.4 Stratified Design with Proportional Allocation 70\u003c\/p\u003e \u003cp\u003e4.5 Optimal Stratified Design for the Total 71\u003c\/p\u003e \u003cp\u003e4.6 Notes About Optimality in Stratification 74\u003c\/p\u003e \u003cp\u003e4.7 Power Allocation 75\u003c\/p\u003e \u003cp\u003e4.8 Optimality and Cost 76\u003c\/p\u003e \u003cp\u003e4.9 Smallest Sample Size 76\u003c\/p\u003e \u003cp\u003e4.10 Construction of the Strata 77\u003c\/p\u003e \u003cp\u003e4.10.1 General Comments 77\u003c\/p\u003e \u003cp\u003e4.10.2 Dividing a Quantitative Variable in Strata 77\u003c\/p\u003e \u003cp\u003e4.11 Stratification Under Many Objectives 79\u003c\/p\u003e \u003cp\u003eExercises 80\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Sampling with Unequal Probabilities \u003c\/b\u003e\u003cb\u003e83\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Auxiliary Variables and Inclusion Probabilities 83\u003c\/p\u003e \u003cp\u003e5.2 Calculation of the Inclusion Probabilities 84\u003c\/p\u003e \u003cp\u003e5.3 General Remarks 85\u003c\/p\u003e \u003cp\u003e5.4 Sampling with Replacement with Unequal Inclusion Probabilities 86\u003c\/p\u003e \u003cp\u003e5.5 Nonvalidity of the Generalization of the Successive Drawing without Replacement 88\u003c\/p\u003e \u003cp\u003e5.6 Systematic Sampling with Unequal Probabilities 89\u003c\/p\u003e \u003cp\u003e5.7 Deville’s Systematic Sampling 91\u003c\/p\u003e \u003cp\u003e5.8 Poisson Sampling 92\u003c\/p\u003e \u003cp\u003e5.9 Maximum Entropy Design 95\u003c\/p\u003e \u003cp\u003e5.10 Rao–Sampford Rejective Procedure 98\u003c\/p\u003e \u003cp\u003e5.11 Order Sampling 100\u003c\/p\u003e \u003cp\u003e5.12 Splitting Method 101\u003c\/p\u003e \u003cp\u003e5.12.1 General Principles 101\u003c\/p\u003e \u003cp\u003e5.12.2 Minimum Support Design 103\u003c\/p\u003e \u003cp\u003e5.12.3 Decomposition into Simple Random Sampling Designs 104\u003c\/p\u003e \u003cp\u003e5.12.4 Pivotal Method 107\u003c\/p\u003e \u003cp\u003e5.12.5 Brewer Method 109\u003c\/p\u003e \u003cp\u003e5.13 Choice of Method 110\u003c\/p\u003e \u003cp\u003e5.14 Variance Approximation 111\u003c\/p\u003e \u003cp\u003e5.15 Variance Estimation 114\u003c\/p\u003e \u003cp\u003eExercises 115\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Balanced Sampling \u003c\/b\u003e\u003cb\u003e119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 119\u003c\/p\u003e \u003cp\u003e6.2 Balanced Sampling: Definition 120\u003c\/p\u003e \u003cp\u003e6.3 Balanced Sampling and Linear Programming 122\u003c\/p\u003e \u003cp\u003e6.4 Balanced Sampling by Systematic Sampling 123\u003c\/p\u003e \u003cp\u003e6.5 Methode of Deville, Grosbras, and Roth 124\u003c\/p\u003e \u003cp\u003e6.6 Cube Method 125\u003c\/p\u003e \u003cp\u003e6.6.1 Representation of a Sampling Design in the form of a Cube 125\u003c\/p\u003e \u003cp\u003e6.6.2 Constraint Subspace 126\u003c\/p\u003e \u003cp\u003e6.6.3 Representation of the Rounding Problem 127\u003c\/p\u003e \u003cp\u003e6.6.4 Principle of the Cube Method 130\u003c\/p\u003e \u003cp\u003e6.6.5 The Flight Phase 130\u003c\/p\u003e \u003cp\u003e6.6.6 Landing Phase by Linear Programming 133\u003c\/p\u003e \u003cp\u003e6.6.7 Choice of the Cost Function 134\u003c\/p\u003e \u003cp\u003e6.6.8 Landing Phase by Relaxing Variables 135\u003c\/p\u003e \u003cp\u003e6.6.9 Quality of Balancing 135\u003c\/p\u003e \u003cp\u003e6.6.10 An Example 136\u003c\/p\u003e \u003cp\u003e6.7 Variance Approximation 137\u003c\/p\u003e \u003cp\u003e6.8 Variance Estimation 140\u003c\/p\u003e \u003cp\u003e6.9 Special Cases of Balanced Sampling 141\u003c\/p\u003e \u003cp\u003e6.10 Practical Aspects of Balanced Sampling 141\u003c\/p\u003e \u003cp\u003eExercise 142\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Cluster and Two-stage Sampling \u003c\/b\u003e\u003cb\u003e143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Cluster Sampling 143\u003c\/p\u003e \u003cp\u003e7.1.1 Notation and Definitions 143\u003c\/p\u003e \u003cp\u003e7.1.2 Cluster Sampling with Equal Probabilities 146\u003c\/p\u003e \u003cp\u003e7.1.3 Sampling Proportional to Size 147\u003c\/p\u003e \u003cp\u003e7.2 Two-stage Sampling 148\u003c\/p\u003e \u003cp\u003e7.2.1 Population, Primary, and Secondary Units 149\u003c\/p\u003e \u003cp\u003e7.2.2 The Expansion Estimator and its Variance 151\u003c\/p\u003e \u003cp\u003e7.2.3 Sampling with Equal Probability 155\u003c\/p\u003e \u003cp\u003e7.2.4 Self-weighting Two-stage Design 156\u003c\/p\u003e \u003cp\u003e7.3 Multi-stage Designs 157\u003c\/p\u003e \u003cp\u003e7.4 Selecting Primary Units with Replacement 158\u003c\/p\u003e \u003cp\u003e7.5 Two-phase Designs 161\u003c\/p\u003e \u003cp\u003e7.5.1 Design and Estimation 161\u003c\/p\u003e \u003cp\u003e7.5.2 Variance and Variance Estimation 162\u003c\/p\u003e \u003cp\u003e7.6 Intersection of Two Independent Samples 163\u003c\/p\u003e \u003cp\u003eExercises 165\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Other Topics on Sampling \u003c\/b\u003e\u003cb\u003e167\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Spatial Sampling 167\u003c\/p\u003e \u003cp\u003e8.1.1 The Problem 167\u003c\/p\u003e \u003cp\u003e8.1.2 Generalized Random Tessellation Stratified Sampling 167\u003c\/p\u003e \u003cp\u003e8.1.3 Using the Traveling Salesman Method 169\u003c\/p\u003e \u003cp\u003e8.1.4 The Local Pivotal Method 169\u003c\/p\u003e \u003cp\u003e8.1.5 The Local Cube Method 169\u003c\/p\u003e \u003cp\u003e8.1.6 Measures of Spread 170\u003c\/p\u003e \u003cp\u003e8.2 Coordination in Repeated Surveys 172\u003c\/p\u003e \u003cp\u003e8.2.1 The Problem 172\u003c\/p\u003e \u003cp\u003e8.2.2 Population, Sample, and Sample Design 173\u003c\/p\u003e \u003cp\u003e8.2.3 Sample Coordination and Response Burden 174\u003c\/p\u003e \u003cp\u003e8.2.4 Poisson Method with Permanent Random Numbers 175\u003c\/p\u003e \u003cp\u003e8.2.5 Kish and Scott Method for Stratified Samples 176\u003c\/p\u003e \u003cp\u003e8.2.6 The Cotton and Hesse Method 176\u003c\/p\u003e \u003cp\u003e8.2.7 The Rivière Method 177\u003c\/p\u003e \u003cp\u003e8.2.8 The Netherlands Method 178\u003c\/p\u003e \u003cp\u003e8.2.9 The Swiss Method 178\u003c\/p\u003e \u003cp\u003e8.2.10 Coordinating Unequal Probability Designs with Fixed Size 181\u003c\/p\u003e \u003cp\u003e8.2.11 Remarks 181\u003c\/p\u003e \u003cp\u003e8.3 Multiple Survey Frames 182\u003c\/p\u003e \u003cp\u003e8.3.1 Introduction 182\u003c\/p\u003e \u003cp\u003e8.3.2 Calculating Inclusion Probabilities 183\u003c\/p\u003e \u003cp\u003e8.3.3 Using Inclusion Probability Sums 184\u003c\/p\u003e \u003cp\u003e8.3.4 Using a Multiplicity Variable 185\u003c\/p\u003e \u003cp\u003e8.3.5 Using a Weighted Multiplicity Variable 186\u003c\/p\u003e \u003cp\u003e8.3.6 Remarks 187\u003c\/p\u003e \u003cp\u003e8.4 Indirect Sampling 187\u003c\/p\u003e \u003cp\u003e8.4.1 Introduction 187\u003c\/p\u003e \u003cp\u003e8.4.2 Adaptive Sampling 188\u003c\/p\u003e \u003cp\u003e8.4.3 Snowball Sampling 188\u003c\/p\u003e \u003cp\u003e8.4.4 Indirect Sampling 189\u003c\/p\u003e \u003cp\u003e8.4.5 The Generalized Weight Sharing Method 190\u003c\/p\u003e \u003cp\u003e8.5 Capture–Recapture 191\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Estimation with a Quantitative Auxiliary Variable \u003c\/b\u003e\u003cb\u003e195\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 The Problem 195\u003c\/p\u003e \u003cp\u003e9.2 Ratio Estimator 196\u003c\/p\u003e \u003cp\u003e9.2.1 Motivation and Definition 196\u003c\/p\u003e \u003cp\u003e9.2.2 Approximate Bias of the Ratio Estimator 197\u003c\/p\u003e \u003cp\u003e9.2.3 Approximate Variance of the Ratio Estimator 198\u003c\/p\u003e \u003cp\u003e9.2.4 Bias Ratio 199\u003c\/p\u003e \u003cp\u003e9.2.5 Ratio and Stratified Designs 199\u003c\/p\u003e \u003cp\u003e9.3 The Difference Estimator 201\u003c\/p\u003e \u003cp\u003e9.4 Estimation by Regression 202\u003c\/p\u003e \u003cp\u003e9.5 The Optimal Regression Estimator 204\u003c\/p\u003e \u003cp\u003e9.6 Discussion of the Three Estimation Methods 205\u003c\/p\u003e \u003cp\u003eExercises 208\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Post-Stratification and Calibration on Marginal Totals \u003c\/b\u003e\u003cb\u003e209\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 209\u003c\/p\u003e \u003cp\u003e10.2 Post-Stratification 209\u003c\/p\u003e \u003cp\u003e10.2.1 Notation and Definitions 209\u003c\/p\u003e \u003cp\u003e10.2.2 Post-Stratified Estimator 211\u003c\/p\u003e \u003cp\u003e10.3 The Post-Stratified Estimator in Simple Designs 212\u003c\/p\u003e \u003cp\u003e10.3.1 Estimator 212\u003c\/p\u003e \u003cp\u003e10.3.2 Conditioning in a Simple Design 213\u003c\/p\u003e \u003cp\u003e10.3.3 Properties of the Estimator in a Simple Design 214\u003c\/p\u003e \u003cp\u003e10.4 Estimation by Calibration on Marginal Totals 217\u003c\/p\u003e \u003cp\u003e10.4.1 The Problem 217\u003c\/p\u003e \u003cp\u003e10.4.2 Calibration on Marginal Totals 218\u003c\/p\u003e \u003cp\u003e10.4.3 Calibration and Kullback–Leibler Divergence 220\u003c\/p\u003e \u003cp\u003e10.4.4 Raking Ratio Estimation 221\u003c\/p\u003e \u003cp\u003e10.5 Example 221\u003c\/p\u003e \u003cp\u003eExercises 224\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Multiple Regression Estimation \u003c\/b\u003e\u003cb\u003e225\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 225\u003c\/p\u003e \u003cp\u003e11.2 Multiple Regression Estimator 226\u003c\/p\u003e \u003cp\u003e11.3 Alternative Forms of the Estimator 227\u003c\/p\u003e \u003cp\u003e11.3.1 Homogeneous Linear Estimator 227\u003c\/p\u003e \u003cp\u003e11.3.2 Projective Form 228\u003c\/p\u003e \u003cp\u003e11.3.3 Cosmetic Form 228\u003c\/p\u003e \u003cp\u003e11.4 Calibration of the Multiple Regression Estimator 229\u003c\/p\u003e \u003cp\u003e11.5 Variance of the Multiple Regression Estimator 230\u003c\/p\u003e \u003cp\u003e11.6 Choice of Weights 231\u003c\/p\u003e \u003cp\u003e11.7 Special Cases 231\u003c\/p\u003e \u003cp\u003e11.7.1 Ratio Estimator 231\u003c\/p\u003e \u003cp\u003e11.7.2 Post-stratified Estimator 231\u003c\/p\u003e \u003cp\u003e11.7.3 Regression Estimation with a Single Explanatory Variable 233\u003c\/p\u003e \u003cp\u003e11.7.4 Optimal Regression Estimator 233\u003c\/p\u003e \u003cp\u003e11.7.5 Conditional Estimation 235\u003c\/p\u003e \u003cp\u003e11.8 Extension to Regression Estimation 236\u003c\/p\u003e \u003cp\u003eExercise 236\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Calibration Estimation \u003c\/b\u003e\u003cb\u003e237\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Calibrated Methods 237\u003c\/p\u003e \u003cp\u003e12.2 Distances and Calibration Functions 239\u003c\/p\u003e \u003cp\u003e12.2.1 The Linear Method 239\u003c\/p\u003e \u003cp\u003e12.2.2 The Raking Ratio Method 240\u003c\/p\u003e \u003cp\u003e12.2.3 Pseudo Empirical Likelihood 242\u003c\/p\u003e \u003cp\u003e12.2.4 Reverse Information 244\u003c\/p\u003e \u003cp\u003e12.2.5 The Truncated Linear Method 245\u003c\/p\u003e \u003cp\u003e12.2.6 General Pseudo-Distance 246\u003c\/p\u003e \u003cp\u003e12.2.7 The Logistic Method 249\u003c\/p\u003e \u003cp\u003e12.2.8 Deville Calibration Function 249\u003c\/p\u003e \u003cp\u003e12.2.9 Roy and Vanheuverzwyn Method 251\u003c\/p\u003e \u003cp\u003e12.3 Solving Calibration Equations 252\u003c\/p\u003e \u003cp\u003e12.3.1 Solving by Newton’s Method 252\u003c\/p\u003e \u003cp\u003e12.3.2 Bound Management 253\u003c\/p\u003e \u003cp\u003e12.3.3 Improper Calibration Functions 254\u003c\/p\u003e \u003cp\u003e12.3.4 Existence of a Solution 254\u003c\/p\u003e \u003cp\u003e12.4 Calibrating on Households and Individuals 255\u003c\/p\u003e \u003cp\u003e12.5 Generalized Calibration 256\u003c\/p\u003e \u003cp\u003e12.5.1 Calibration Equations 256\u003c\/p\u003e \u003cp\u003e12.5.2 Linear Calibration Functions 257\u003c\/p\u003e \u003cp\u003e12.6 Calibration in Practice 258\u003c\/p\u003e \u003cp\u003e12.7 An Example 259\u003c\/p\u003e \u003cp\u003eExercises 260\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Model-Based approach \u003c\/b\u003e\u003cb\u003e263\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Model Approach 263\u003c\/p\u003e \u003cp\u003e13.2 The Model 263\u003c\/p\u003e \u003cp\u003e13.3 Homoscedastic Constant Model 267\u003c\/p\u003e \u003cp\u003e13.4 Heteroscedastic Model 1 Without Intercept 267\u003c\/p\u003e \u003cp\u003e13.5 Heteroscedastic Model 2 Without Intercept 269\u003c\/p\u003e \u003cp\u003e13.6 Univariate Homoscedastic Linear Model 270\u003c\/p\u003e \u003cp\u003e13.7 Stratified Population 271\u003c\/p\u003e \u003cp\u003e13.8 Simplified Versions of the Optimal Estimator 273\u003c\/p\u003e \u003cp\u003e13.9 Completed Heteroscedasticity Model 276\u003c\/p\u003e \u003cp\u003e13.10 Discussion 277\u003c\/p\u003e \u003cp\u003e13.11 An Approach that is Both Model- and Design-based 277\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Estimation of Complex Parameters \u003c\/b\u003e\u003cb\u003e281\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Estimation of a Function of Totals 281\u003c\/p\u003e \u003cp\u003e14.2 Variance Estimation 282\u003c\/p\u003e \u003cp\u003e14.3 Covariance Estimation 283\u003c\/p\u003e \u003cp\u003e14.4 Implicit Function Estimation 283\u003c\/p\u003e \u003cp\u003e14.5 Cumulative Distribution Function and Quantiles 284\u003c\/p\u003e \u003cp\u003e14.5.1 Cumulative Distribution Function Estimation 284\u003c\/p\u003e \u003cp\u003e14.5.2 Quantile Estimation: Method 1 284\u003c\/p\u003e \u003cp\u003e14.5.3 Quantile Estimation: Method 2 285\u003c\/p\u003e \u003cp\u003e14.5.4 Quantile Estimation: Method 3 287\u003c\/p\u003e \u003cp\u003e14.5.5 Quantile Estimation: Method 4 288\u003c\/p\u003e \u003cp\u003e14.6 Cumulative Income, Lorenz Curve, and Quintile Share Ratio 288\u003c\/p\u003e \u003cp\u003e14.6.1 Cumulative Income Estimation 288\u003c\/p\u003e \u003cp\u003e14.6.2 Lorenz Curve Estimation 289\u003c\/p\u003e \u003cp\u003e14.6.3 Quintile Share Ratio Estimation 289\u003c\/p\u003e \u003cp\u003e14.7 Gini Index 290\u003c\/p\u003e \u003cp\u003e14.8 An Example 291\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Variance Estimation by Linearization \u003c\/b\u003e\u003cb\u003e295\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 295\u003c\/p\u003e \u003cp\u003e15.2 Orders of Magnitude in Probability 295\u003c\/p\u003e \u003cp\u003e15.3 Asymptotic Hypotheses 300\u003c\/p\u003e \u003cp\u003e15.3.1 Linearizing a Function of Totals 301\u003c\/p\u003e \u003cp\u003e15.3.2 Variance Estimation 303\u003c\/p\u003e \u003cp\u003e15.4 Linearization of Functions of Interest 303\u003c\/p\u003e \u003cp\u003e15.4.1 Linearization of a Ratio 303\u003c\/p\u003e \u003cp\u003e15.4.2 Linearization of a Ratio Estimator 304\u003c\/p\u003e \u003cp\u003e15.4.3 Linearization of a Geometric Mean 305\u003c\/p\u003e \u003cp\u003e15.4.4 Linearization of a Variance 305\u003c\/p\u003e \u003cp\u003e15.4.5 Linearization of a Covariance 306\u003c\/p\u003e \u003cp\u003e15.4.6 Linearization of a Vector of Regression Coefficients 307\u003c\/p\u003e \u003cp\u003e15.5 Linearization by Steps 308\u003c\/p\u003e \u003cp\u003e15.5.1 Decomposition of Linearization by Steps 308\u003c\/p\u003e \u003cp\u003e15.5.2 Linearization of a Regression Coefficient 308\u003c\/p\u003e \u003cp\u003e15.5.3 Linearization of a Univariate Regression Estimator 309\u003c\/p\u003e \u003cp\u003e15.5.4 Linearization of a Multiple Regression Estimator 309\u003c\/p\u003e \u003cp\u003e15.6 Linearization of an Implicit Function of Interest 310\u003c\/p\u003e \u003cp\u003e15.6.1 Estimating Equation and Implicit Function of Interest 310\u003c\/p\u003e \u003cp\u003e15.6.2 Linearization of a Logistic Regression Coefficient 311\u003c\/p\u003e \u003cp\u003e15.6.3 Linearization of a Calibration Equation Parameter 313\u003c\/p\u003e \u003cp\u003e15.6.4 Linearization of a Calibrated Estimator 313\u003c\/p\u003e \u003cp\u003e15.7 Influence Function Approach 314\u003c\/p\u003e \u003cp\u003e15.7.1 Function of Interest, Functional 314\u003c\/p\u003e \u003cp\u003e15.7.2 Definition 315\u003c\/p\u003e \u003cp\u003e15.7.3 Linearization of a Total 316\u003c\/p\u003e \u003cp\u003e15.7.4 Linearization of a Function of Totals 316\u003c\/p\u003e \u003cp\u003e15.7.5 Linearization of Sums and Products 317\u003c\/p\u003e \u003cp\u003e15.7.6 Linearization by Steps 318\u003c\/p\u003e \u003cp\u003e15.7.7 Linearization of a Parameter Defined by an Implicit Function 318\u003c\/p\u003e \u003cp\u003e15.7.8 Linearization of a Double Sum 319\u003c\/p\u003e \u003cp\u003e15.8 Binder’s Cookbook Approach 321\u003c\/p\u003e \u003cp\u003e15.9 Demnati and Rao Approach 322\u003c\/p\u003e \u003cp\u003e15.10 Linearization by the Sample Indicator Variables 324\u003c\/p\u003e \u003cp\u003e15.10.1 The Method 324\u003c\/p\u003e \u003cp\u003e15.10.2 Linearization of a Quantile 326\u003c\/p\u003e \u003cp\u003e15.10.3 Linearization of a Calibrated Estimator 327\u003c\/p\u003e \u003cp\u003e15.10.4 Linearization of a Multiple Regression Estimator 328\u003c\/p\u003e \u003cp\u003e15.10.5 Linearization of an Estimator of a Complex Function with Calibrated Weights 329\u003c\/p\u003e \u003cp\u003e15.10.6 Linearization of the Gini Index 330\u003c\/p\u003e \u003cp\u003e15.11 Discussion on Variance Estimation 331\u003c\/p\u003e \u003cp\u003eExercises 331\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Treatment of Nonresponse \u003c\/b\u003e\u003cb\u003e333\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Sources of Error 333\u003c\/p\u003e \u003cp\u003e16.2 Coverage Errors 334\u003c\/p\u003e \u003cp\u003e16.3 Different Types of Nonresponse 334\u003c\/p\u003e \u003cp\u003e16.4 Nonresponse Modeling 335\u003c\/p\u003e \u003cp\u003e16.5 Treating Nonresponse by Reweighting 336\u003c\/p\u003e \u003cp\u003e16.5.1 Nonresponse Coming from a Sample 336\u003c\/p\u003e \u003cp\u003e16.5.2 Modeling the Nonresponse Mechanism 337\u003c\/p\u003e \u003cp\u003e16.5.3 Direct Calibration of Nonresponse 339\u003c\/p\u003e \u003cp\u003e16.5.4 Reweighting by Generalized Calibration 341\u003c\/p\u003e \u003cp\u003e16.6 Imputation 342\u003c\/p\u003e \u003cp\u003e16.6.1 General Principles 342\u003c\/p\u003e \u003cp\u003e16.6.2 Imputing From an Existing Value 342\u003c\/p\u003e \u003cp\u003e16.6.3 Imputation by Prediction 342\u003c\/p\u003e \u003cp\u003e16.6.4 Link Between Regression Imputation and Reweighting 343\u003c\/p\u003e \u003cp\u003e16.6.5 Random Imputation 345\u003c\/p\u003e \u003cp\u003e16.7 Variance Estimation with Nonresponse 347\u003c\/p\u003e \u003cp\u003e16.7.1 General Principles 347\u003c\/p\u003e \u003cp\u003e16.7.2 Estimation by Direct Calibration 348\u003c\/p\u003e \u003cp\u003e16.7.3 General Case 349\u003c\/p\u003e \u003cp\u003e16.7.4 Variance for Maximum Likelihood Estimation 350\u003c\/p\u003e \u003cp\u003e16.7.5 Variance for Estimation by Calibration 353\u003c\/p\u003e \u003cp\u003e16.7.6 Variance of an Estimator Imputed by Regression 356\u003c\/p\u003e \u003cp\u003e16.7.7 Other Variance Estimation Techniques 357\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Summary Solutions to the Exercises \u003c\/b\u003e\u003cb\u003e359\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eBibliography 379\u003c\/p\u003e \u003cp\u003eAuthor Index 405\u003c\/p\u003e \u003cp\u003eSubject Index 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