Chapter
1.8 SAMPLING FROM HYPOTHETICAL POPULATIONS
1.8.1 Sampling From a Uniform Population
1.8.2 Sampling From a Normal Population
1.8.3 Sampling From a Binomial Population
2 - Unified Sampling Theory: Design-Based Inference
2.2 DEFINITIONS AND TERMINOLOGIES
2.2.1 Noninformative and Adaptive (Sequential) Sampling Designs
2.2.2 Estimator and Estimate
2.2.4 Mean Square Error and Variance
2.2.5 Uniformly Minimum Variance Unbiased Estimator
2.3 LINEAR UNBIASED ESTIMATORS
2.3.1 Conditions of Unbiasedness
2.3.2 Horvitz-Thompson Estimator
2.3.3 Hansen-Hurwitz Estimator
2.3.4 Unbiased Ratio Estimator
2.3.5 Difference and Generalized Difference Estimator
2.4 PROPERTIES OF THE HORVITZ-THOMPSON ESTIMATOR
2.5 NONEXISTENCE THEOREMS
2.5.1 Unicluster Sampling Design
2.5.2 Class of Linear Homogeneous Unbiased Estimators
2.5.3 Optimality of the Horvitz-Thompson Estimator
2.5.4 Class of All Unbiased Estimators
2.5.5 Class of Linear Unbiased Estimators
2.6 ADMISSIBLE ESTIMATORS
2.7 SUFFICIENCY IN FINITE POPULATION
2.7.1 Sufficiency and Likelihood
2.7.2 Minimal Sufficient Statistic
2.7.3 Rao-Blackwellization
2.8.2 Uniformly Minimum Variance Unbiased Strategy
2.8.3 Admissible Strategies
3 - Simple Random Sampling
3.2 SIMPLE RANDOM SAMPLING WITHOUT REPLACEMENT
3.2.2 Estimation of Population Mean and Variance
3.2.3 Estimation of Population Covariance
3.2.4 Estimation of Population Proportion
3.2.5 Estimation of Domain Mean and Total
3.3 SIMPLE RANDOM SAMPLING WITH REPLACEMENT
3.3.2 Estimation of the Population Mean and Variance
3.3.3 Estimation of Population Proportion
3.3.4 Rao-Blackwellization
3.4.1 Confidence Intervals for Mean and Proportion
3.4.1.1 Large Sample Size
3.4.1.2 Small Sample Size
3.5 DETERMINATION OF SAMPLE SIZE
3.5.1 Consideration of the Cost of a Survey
3.5.2 Consideration of the Efficiency of Estimators
3.5.2.2 Given Coefficient of Variation
3.5.2.3 Given Margin of Permissible Error
3.5.3 Use of Chebyshev Inequality
3.6.1 Simple Random Sampling Without Replacement
3.6.2 Simple Random Sampling With Replacement
4.2 LINEAR SYSTEMATIC SAMPLING
4.2.1 Linear Systematic Sampling With N/n=k an Integer
4.2.2 Linear Systematic Sampling With N/n=k Not an Integer
4.2.3 Estimation of the Population Mean and Its Variance
4.2.4 Nonexistence of Unbiased Variance Estimator
4.3 EFFICIENCY OF SYSTEMATIC SAMPLING
4.3.1 Comparison With Simple Random Sampling
4.3.2 Comparison With Stratified Sampling
4.3.3 Random Arrangement of Units
4.3.4 Population With Linear Trend
4.3.4.2 Balanced Systematic Sampling
4.3.5 Population With Periodic Variation
4.3.6 Autocorrelated Population
4.4 LINEAR SYSTEMATIC SAMPLING USING FRACTIONAL INTERVAL
4.5 CIRCULAR SYSTEMATIC SAMPLING
4.5.1 Circular Systematic Sampling With k=N/n as an Integer
4.5.2 Circular Systematic Sampling With N/n is Not an Integer
4.6.1 Single Systematic Sample
4.6.1.1 Random Arrangements of Units
4.6.1.2 Stratified Sampling With One Unit Per Stratum
4.6.1.3 Presence of Linear Trend
4.6.1.4 Presence of Autocorrelation Between Successive Units
4.6.1.5 Splitting of a Systematic Sample
4.6.2 Several Systematic Samples
4.7 TWO-DIMENSIONAL SYSTEMATIC SAMPLING
5 - Unequal Probability Sampling
5.2 PROBABILITY PROPORTIONAL TO SIZE WITH REPLACEMENT SAMPLING SCHEME
5.2.1 Cumulative Total Method
5.2.3 Hansen-Hurwitz Estimator and its Variance
5.2.4 Rao-Blackwellization
5.3 PROBABILITY PROPORTIONAL TO SIZE WITHOUT REPLACEMENT SAMPLING SCHEME
5.3.1 Raj's Estimator and its Variance
5.3.2 Rao-Blackwellization
5.3.2.1 Murthy's Estimator
5.4 INCLUSION PROBABILITY PROPORTIONAL TO MEASURE OF SIZE SAMPLING SCHEME
5.4.1 Inclusion Probability Proportional to Measure of Size Sampling With n=2
5.4.1.1 Brewer's Sampling Scheme
5.4.1.2 Durbin's Sampling Scheme
5.4.1.3 Hanurav's Sampling Scheme
5.4.2 Inclusion Probability Proportional to Measure of Size Sampling with n﹥2
5.4.2.1 Lahiri-Midzuno-Sen Sampling Design
5.4.2.2 Probability Proportionate to Size Systematic Sampling Scheme
5.4.2.3 Sampford's Sampling Scheme
5.4.2.3.1 Comparison of Efficiency
5.4.2.4 Poisson (or Bernoulli) Sampling
5.4.2.5 Use of Combinatorics
5.4.2.6 The Nearest Proportional to Size Sampling
5.5 PROBABILITY PROPORTIONAL TO AGGREGATE SIZE WITHOUT REPLACEMENT
5.6 RAO-HARTLEY-COCHRAN SAMPLING SCHEME
5.7 COMPARISON OF UNEQUAL (VARYING) PROBABILITY SAMPLING DESIGNS
6 - Inference Under Superpopulation Model
6.2.2 Noninformative Sampling Design
6.2.3 Design-Unbiased (or p-Unbiased) Estimator
6.2.4 Model-Unbiased (or ξ-Unbiased) Estimator
6.2.5 Model Design-Unbiased (or pξ-Unbiased) Estimator
6.2.6 Design-Based Inference
6.2.7 Model-Based Inference
6.2.8 Model-Assisted Inference
6.3 MODEL-ASSISTED INFERENCE
6.3.1 Optimal Design-Unbiased Predictors
6.3.1.1 Product Measure Model
6.3.1.2 Equicorrelation Model
6.3.1.3 Transformation Model
6.3.2 Optimal Model Design-Unbiased Prediction
6.3.4 Random Permutation Model
6.4 MODEL-BASED INFERENCE
6.4.1 Optimal Model-Unbiased Prediction
6.4.1.1 Product Measure Model
6.4.1.2 Transformation Model
6.4.1.3 Multiple Regression Model
6.5 ROBUSTNESS OF DESIGNS AND PREDICTORS
6.5.1 Robustness of Predictors
6.5.2 Balanced Sampling Design
6.5.3 Polynomial Regression Model
6.5.4 Balanced Sample of Order k
6.5.5 Optimality of Balanced Sampling
6.7 COMPARISON OF STRATEGIES UNDER SUPERPOPULATION MODELS
6.7.1 Hansen-Hurwitz Strategy With Others
6.7.2 Horvitz-Thompson and Rao-Hartley-Cochran Strategy
6.7.3 Horvitz-Thompson and Lahiri-Midzuno-Sen Strategy
6.7.4 Rao-Hartley-Cochran and Lahiri-Midzuno-Sen Strategy
7.2 DEFINITION OF STRATIFIED SAMPLING
7.3 ADVANTAGES OF STRATIFIED SAMPLING
7.4.1 Estimation of Population Mean
7.4.1.1 Arbitrary Fixed Sample Size Design
7.4.1.2 Simple Random Sampling Without Replacement
7.4.1.3 Probability Proportional to Size With Replacement Sampling
7.4.1.4 Simple Random Sampling With Replacement
7.4.2 Estimation of Population Proportion
7.4.2.1 Simple Random Sampling Without Replacement
7.4.2.2 Simple Random Sampling With Replacement
7.4.3 Interval Estimation
7.5 ALLOCATION OF SAMPLE SIZE
7.5.1 Optimum Allocation for Fixed Cost
7.5.2 Optimum Allocation for Fixed Variance
7.5.3 Simple Random Sampling Without Replacement
7.5.4 Simple Random Sampling With Replacement
7.5.5 Probability Proportional to Size With Replacement Sampling
7.5.6 Neyman Optimum Allocation
7.5.7 Proportional Allocation
7.6 COMPARISON BETWEEN STRATIFIED AND UNSTRATIFIED SAMPLING
7.6.1 Simple Random Sampling Without Replacement
7.6.2 Probability Proportional to Size With Replacement Sampling
7.6.3 Inclusion Probability Proportional to Size Sampling Scheme
7.7 CONSTRUCTION OF STRATA
7.7.1 Optimum Points of Stratification
7.7.1.1 Proportional Allocation
7.7.1.2 Optimum Allocation
7.7.2 Dalenius and Hodges's Approximation
7.8 ESTIMATION OF GAIN DUE TO STRATIFICATION
7.8.1 Simple Random Sampling Without Replacement
7.8.2 Probability Proportional to Size With Replacement Sampling
8 - Ratio Method of Estimation
8.2 RATIO ESTIMATOR FOR POPULATION RATIO
8.2.1 Exact Expression of Bias and Mean-Square Error
8.2.2 Approximate Expression of Bias and Mean-Square Errors
8.3 RATIO ESTIMATOR FOR POPULATION TOTAL
8.3.1 Efficiency of the Ratio Estimator
8.3.2 Optimality of the Ratio Estimator
8.4 BIASES AND MEAN-SQUARE ERRORS FOR SPECIFIC SAMPLING DESIGNS
8.4.1 Fixed Effective Sample Size (n) Design
8.4.2 Simple Random Sampling Without Replacement
8.4.3 Probability Proportional to Size With Replacement
8.4.4 Simple Random Sampling With Replacement
8.6 UNBIASED RATIO, ALMOST UNBIASED RATIO, AND UNBIASED RATIO-TYPE ESTIMATORS
8.6.1 Unbiased Ratio Estimator
8.6.2 Almost Unbiased Ratio Estimator
8.6.3 Unbiased Ratio-Type Estimators
8.6.4 Hartley-Ross Estimator
8.7 RATIO ESTIMATOR FOR STRATIFIED SAMPLING
8.7.1 Separate Ratio Estimator
8.7.2 Combined Ratio Estimator
8.7.3 Comparison Between the Separate and Combined Ratio Estimators
8.8 RATIO ESTIMATOR FOR SEVERAL AUXILIARY VARIABLES
8.8.1 Simple Random Sampling Without Replacement
9 - Regression, Product, and Calibrated Methods of Estimation
9.3.1 Exact Expression of Bias
9.3.2 Approximate Expression of Bias
9.3.2.1 Bias Under Simple Random Sampling Without Replacement
9.3.3 Approximate Expression of the Mean Square Error
9.3.4 Mean Square Errors for Some Sampling Designs
9.3.4.1 Arbitrary Fixed Effective Sample Size Design
9.3.4.2 Simple Random Sampling Without Replacement
9.3.5 Efficiency of Regression Estimator
9.3.5.1 Comparison With the Ratio Estimator
9.3.6 Optimality of the Regression Estimator
9.3.7 Unbiased Regression Estimator
9.3.7.1 Singh and Srivastava Sampling Scheme
9.3.8 Stratified Regression Estimator
9.3.8.1 Separate Regression Estimator
9.3.8.2 Combined Regression Estimator
9.3.8.3 Comparison Between Combined and Separate Regression Estimators
9.3.9 Regression Estimator for Several Auxiliary Variables
9.3.9.1 Multivariate Regression Estimator
9.3.9.2 Two Auxiliary Variables
9.3.9.3 Raj's Regression Estimator
9.4 PRODUCT METHOD OF ESTIMATION
9.4.1 Bias of the Product Estimator
9.4.2 Mean Square Error of the Product Estimator
9.4.3 Comparison With the Conventional Estimator
9.4.4 Product Estimator for a Few Sampling Designs
9.4.4.1 Fixed Effective Sample Size Design
9.4.4.2 Simple Random Sampling Without Replacement
9.4.5 Unbiased Product Type Estimators
9.4.5.1 Simple Random Sampling Without Replacement
9.5 COMPARISON BETWEEN THE RATIO, REGRESSION, PRODUCT, AND CONVENTIONAL ESTIMATORS
9.6 DUAL TO RATIO ESTIMATOR
9.6.1 Bias of the Dual Estimator
9.6.2 Mean Square Error of the Dual Estimator
9.6.3 Comparison With Other Estimators
9.6.3.1 Conventional Estimator
9.6.3.3 Product Estimator
9.7 CALIBRATION ESTIMATORS
9.7.1 Efficiency of Calibrated Estimator
9.7.2 Calibration Estimator for Several Auxiliary Variables
10.2 TWO-PHASE SAMPLING FOR ESTIMATION
10.2.1 Difference Method of Estimation
10.2.1.1 Arbitrary Sampling Design
10.2.1.2 Simple Random Sampling Without Replacement
10.2.1.3 Efficiency Under Simple Random Sampling Without Replacement
10.2.1.4 Probability Proportional to Size With Replacement Sampling
10.2.2 Ratio Method of Estimation
10.2.2.1 Approximate Expression of Bias
10.2.2.2 Approximate Expression of Mean Square Error
10.2.2.3 Simple Random Sampling Without Replacement
10.2.2.4 Optimal Allocation Under Simple Random Sampling Without Replacement
10.2.3 Regression Method of Estimation
10.2.3.1 Approximate Expressions of Bias and Mean Square Errors
10.2.3.2 Arbitrary Sampling Design
10.2.3.3 Simple Random Sampling Without Replacement
10.2.3.4 Optimum Allocation
10.3 TWO-PHASE SAMPLING FOR STRATIFICATION
10.3.1 Estimation of Mean and Variance
10.3.2 Proportional Allocation
10.3.3 Estimation of Proportion
10.3.4 Optimum Allocation of Sample Sizes
10.4 TWO-PHASE SAMPLING FOR SELECTION OF SAMPLE
10.4.1 Probability Proportional to Size With Replacement Sampling
10.4.2 Rao-Hartley-Cochran Sampling
10.5 TWO-PHASE SAMPLING FOR STRATIFICATION AND SELECTION OF SAMPLE
11.2 ESTIMATION OF MEAN FOR THE MOST RECENT OCCASION
11.2.1 Sampling on Two Occasions
11.2.1.2 General Method of Estimation
11.2.1.3 Simple Random Sampling Without Replacement
11.2.1.3.1 Optimum Allocation of the Matched Sample
11.2.1.4 Probability Proportional to Size With Replacement Sampling
11.2.1.5 Simple Random Sampling With Replacement
11.2.1.6 Sampling Over Two Occasions: Stratifying the Initial Sample
11.2.2 Sampling More Than Two Occasions
11.2.2.1 Probability Proportional to Size With Replacement Sampling
11.2.2.2 Simple Random Sampling With Replacement
11.2.2.2.1 Estimator for the Total on the hth Occasion
11.3 ESTIMATION OF CHANGE OVER TWO OCCASIONS
11.3.1 Simple Random Sampling Without Replacement
11.4 ESTIMATION OF MEAN OF MEANS
11.4.1 Simple Random Sampling Without Replacement
12.2 ESTIMATION OF POPULATION TOTAL AND VARIANCE
12.2.1 Arbitrary Sampling Design
12.2.2 Simple Random Sampling Without Replacement
12.3 EFFICIENCY OF CLUSTER SAMPLING
12.3.1 Optimum Choice of Cluster Size
12.4 PROBABILITY PROPORTIONAL TO SIZE WITH REPLACEMENT SAMPLING
12.4.1 Simple Random Sampling With Replacement
12.5 ESTIMATION OF MEAN PER UNIT
12.5.1.1 Arbitrary Sampling Design
12.5.1.2 Simple Random Sampling Without Replacement
13.2 TWO-STAGE SAMPLING SCHEME
13.3 ESTIMATION OF THE POPULATION TOTAL AND VARIANCE
13.3.1 First-Stage Arbitrary Sampling Designs and Second-Stage Simple Random Sampling Without Replacement
13.3.2 Simple Random Sampling Without Replacement Both the Stages
13.3.3 First-Stage Rao--Hartley--Cochran and Second-Stage Simple Random Sampling Without Replacement
13.4 FIRST-STAGE UNITS ARE SELECTED BY PPSWR SAMPLING SCHEME
13.4.1 Simple Random Sampling With Replacement
13.4.2 Raj Estimator for Multi-Stage Sampling
13.5 MODIFICATION OF VARIANCE ESTIMATORS
13.5.1 Srinath and Hidiroglou Modification
13.5.2 Arnab Modification
13.6 MORE THAN TWO-STAGE SAMPLING
13.6.1 Three-Stage Sampling
13.7 ESTIMATION OF MEAN PER UNIT
13.7.1 Simple Random Sampling Without Replacement
13.8.1 Fixed Expected Cost
13.9 SELF -WEIGHTING DESIGN
14 - Variance/Mean Square Estimation
14.2 LINEAR UNBIASED ESTIMATORS
14.2.1 Conditions of Unbiased Estimation of Variance
14.3 NONNEGATIVE VARIANCE/MEAN SQUARE ESTIMATION
14.3.1.1 Horvitz-Thompson Estimator
14.3.1.2 Hansen-Hurwitz Estimator
14.3.1.3 Murthy's Estimator
14.3.1.4 Unbiased Ratio Estimator
14.3.1.5 Ordinary Ratio Estimator
14.3.1.6 Hartley-Ross Estimator
15.2 SOURCES OF NONSAMPLING ERRORS
15.3 CONTROLLING OF NONSAMPLING ERRORS
15.4 TREATMENT OF NONRESPONSE ERROR
15.4.1 Poststratification
15.4.1.1 Hansen-Hurwitz Method
15.4.1.1.1 Optimum Value of ν and n
15.4.2 Use of Response Probabilities
15.4.2.1 Classification of Response Probabilities
15.4.3 Politz and Simmons Method
15.4.4.1 Problems of Imputation
15.4.5 Multiple Imputation
15.4.6 Bayesian Imputation
15.4.6.1 Wang et al. Method
15.4.6.2 Schenker and Welsh Method
15.4.7 Subsampling Method
15.4.7.1 Arnab and Singh Method
15.4.7.1.1 Simple Random Sampling Without Replacement
15.4.7.2 Singh and Singh Method
15.5.1 Measurement Bias and Variance
15.5.1.1 Simple Random Sampling Without Replacement
15.5.2 Interpenetrating Subsamples
16 - Randomized Response Techniques
16.2 RANDOMIZED RESPONSE TECHNIQUES FOR QUALITATIVE CHARACTERISTICS
16.2.1 Warner's Technique: the Pioneering Method
16.2.1.1 Estimation of Proportion
16.2.1.2 Comparison With Direct Response Surveys
16.2.1.3 Maximum Likelihood Estimation of Proportion
16.2.2 Greenberg et al.: Unrelated Question Method
16.2.2.1 Estimation of Proportion
16.2.4 Mangat and Singh Model
16.3 EXTENSION TO MORE THAN ONE CATEGORIES
16.3.1 Liu and Chow's Technique
16.3.1.1 Estimation of Proportions
16.4 RANDOMIZED RESPONSE TECHNIQUES FOR QUANTITATIVE CHARACTERISTICS
16.4.1 Eriksson's Technique
16.4.3 Christofides's Model
16.4.4 Eichhorn and Hayre's Model
16.4.5 Franklin's Randomized Response Technique
16.4.6 Chaudhuri's Randomized Response
16.5 GENERAL METHOD OF ESTIMATION
16.5.1 Estimation of Total and Variance
16.5.1.1 Horvitz-Thomson Estimator
16.5.1.2 Simple Random Sampling Without Replacement
16.5.1.3 Rao-Hartley-Cochran Sampling
16.5.1.4 Probability Proportional to Aggregate Size Sampling
16.5.1.5 Probability Proportional to Size With Replacement Sampling
16.5.1.6 Simple Random Sampling With Replacement
16.6 OPTIONAL RANDOMIZED RESPONSE TECHNIQUES
16.6.1 Full Optional Randomized Response Technique
16.6.1.1 Estimation of Population Total
16.6.1.2 Horvitz-Thompson Estimator Based on a Fixed Sample Size Design
16.6.1.3 Simple Random Sampling Without Replacement
16.6.1.4 Rao-Hartley-Cochran Sampling
16.6.1.5 Probability Proportional to Size With Replacement Sampling
16.6.1.6 Simple Random Sampling With Replacement
16.6.2 Partial Optional Randomized Response Technique
16.6.2.1 Gupta et al. Model
16.7 MEASURE OF PROTECTION OF PRIVACY
16.7.1 Qualitative Characteristic With ``Yes-No'' Response
16.7.1.1 Leysieffer and Warner's Measure
16.7.1.3 Anderson's Measure
16.7.2 Quantitative Characteristics
16.8 OPTIMALITY UNDER SUPERPOPULATION MODEL
16.8.1 Product Measure Model
16.8.2 Equicorrelation Model
16.8.3 Construction of an Optimal Randomized Response Technique
17 - Domain and Small Area Estimation
17.2.1 Horvitz-Thomson Estimator
17.3 SMALL AREA ESTIMATION
17.3.1 Symptomatic Accounting Technique
17.3.1.1 Vital Rates Method
17.3.1.2 Composite Method
17.3.1.3 Census Component Method
17.3.1.4 Housing Unit Method
17.3.1.5 Ratio Correlation Method
17.3.1.6 Difference Correlation Method
17.3.3 Synthetic Estimation
17.3.4 Composite Estimation
17.3.5 Borrowing Strength From Related Areas
17.3.5.1 Synthetic Estimator
17.3.5.2 Generalized Regression Estimator
17.3.5.3 Composite Estimator
17.3.6.1 General Linear Mixed Model
17.3.6.2 Nested Error Regression Model
17.3.6.3 Area-Level Model
17.3.6.4 Fay-Herriot Model
17.3.7 Empirical Best Linear Unbiased Prediction, Empirical Bayes, and Hierarchical Bayes Methods
17.3.7.1 Empirical Best Linear Unbiased Prediction
17.3.7.1.1 Onefold Nested Error Regression Model
17.3.7.1.2 Fay-Herriot Model
17.3.7.2 Empirical Bayes Approach
17.3.7.3 Hierarchical Bayes Approach
18 - Variance Estimation: Complex Survey Designs
18.2 LINEARIZATION METHOD
18.2.2 Coefficient of Variation
18.3.1 Simple Random Sampling With Replacement
18.3.2 Simple Random Sampling Without Replacement
18.3.3 Varying Probability Sampling
18.3.4 Multistage Sampling
18.4.1 Jackknife Method for an Infinite Population
18.4.1.1 Higher-Order Jackknife Estimator
18.4.1.2 Generalized Jackknife Estimator
18.4.2 Jackknife Method for a Finite Population
18.4.2.1 Probability Proportional to Size With Replacement Sampling
18.4.2.1.1 Bias of Jackknife Variance Estimator
18.4.2.2 Simple Random Sampling With Replacement
18.4.2.3 Inclusion Probability Proportional to Size or πps Sampling Design
18.4.2.3.1 Bias of Jackknife Variance Estimator
18.4.2.4 Simple Random Sampling Without Replacement
18.4.2.5 Regression Estimator
18.4.2.6 Numerical Example
18.5 BALANCED REPEATED REPLICATION METHOD
18.5.1 Stratified Sampling With nh=2
18.5.2 Methods of Variance Estimation
18.5.3.1 Population Ratio
18.5.3.2 Inclusion Probability Proportional to Size Sampling Scheme
18.5.4.2 Population Ratio
18.5.4.3 Correlation Coefficient
18.5.5.1 Grouped Balanced Half-Sample Method
18.5.5.2 Subdivision of Strata
18.5.6 Stratified Multistage Sampling
18.6.1 Bootstrap for Infinite Population
18.6.1.1 Bootstrap Confidence Interval
18.6.1.1.1 Percentile Method
18.6.1.1.2 Bootstrap t-Method
18.6.2 Bootstrap for Finite Population
18.6.2.1 Bootstrap for Simple Random Sampling With Replacement
18.6.2.2 Rescaling Bootstrap
18.6.2.3 Bootstrap Without Replacement Method
18.6.2.4 Mirror-Match Bootstrap
18.6.2.5 Bootstrap for Varying Probability Sampling Without Replacement
18.7 GENERALIZED VARIANCE FUNCTIONS
18.7.1 Generalized Variance Function Model
18.7.2 Justification of Generalized Variance Function Model
18.7.3 Generalized Variance Function Method for Variance Estimation
18.7.4 Applicability Generalized Variance Function Model
18.8 COMPARISON BETWEEN THE VARIANCE ESTIMATORS
19 - Complex Surveys: Categorical Data Analysis
19.2 PEARSONIAN CHI-SQUARE TEST FOR GOODNESS OF FIT
19.3 GOODNESS OF FIT FOR A GENERAL SAMPLING DESIGN
19.3.1 Wald Statistic for Goodness of Fit
19.3.1.1 Simple Random Sampling With Replacement
19.3.2 Generalized Pearsonian Chi-Square Statistic
19.3.3 Modifications to XG2
19.3.3.1 Use of Maximum or Minimum Eigenvalues
19.3.3.2 Rao-Scott First-Order Corrections
19.3.3.3 Rao-Scott Second-Order Corrections
19.3.3.4 Fellegi Correction
19.3.4 Simple Random Sampling Without Replacement
19.3.5 Stratified Sampling
19.3.6 Two-Stage Sampling
19.4 TEST OF INDEPENDENCE
19.4.3 Modified Chi-Square
19.5 TESTS OF HOMOGENEITY
19.5.2 Modified Chi-Square Statistics
19.6 CHI-SQUARE TEST BASED ON SUPERPOPULATION MODEL
20 - Complex Survey Design: Regression Analysis
20.2 DESIGN-BASED APPROACH
20.2.1 Estimation of Variance
20.2.2 Logistic Regression
20.3 MODEL-BASED APPROACH
20.3.1 Performances of the Proposed Estimators
20.3.2 Variance Estimation
20.3.3 Multistage Sampling
20.3.4 Separate Regression for Each First-Stage Unit
21.2 RANKED SET SAMPLING BY SIMPLE RANDOM SAMPLING WITH REPLACEMENT METHOD
21.2.1 A Fundamental Equality
21.2.2 Estimation of the Mean
21.2.3 Precision of the Ranked Set Sampling
21.2.4 Optimum Value of m
21.2.5 Optimum Allocation
21.2.5.1 Right-Tail Allocation Model
21.2.6.1 Moment of the Judgment Order Statistic
21.2.7 Estimation of Population Variance
21.2.7.1 Efficiency of σ^〈rss〉2
21.2.8 Use of Concomitant Variables
21.2.8.1 Relative Precision of μ^reg
21.3 SIMPLE RANDOM SAMPLING WITHOUT REPLACEMENT
21.3.1 Relative Precision
21.4 SIZE-BIASED PROBABILITY OF SELECTION
22 - Estimating Functions
22.2 ESTIMATING FUNCTION AND ESTIMATING EQUATIONS
22.2.1 Optimal Properties of Estimating Functions
22.3 ESTIMATING FUNCTION FROM SUPERPOPULATION MODEL
22.3.1 Optimal and Linearly Optimal Estimating Functions
22.4 ESTIMATING FUNCTION FOR A SURVEY POPULATION
22.5.1 Confidence Interval for θ
22.5.1.1 Confidence Interval for Survey Parameter θN
22.5.1.2 Stratified Sampling
22.5.1.3 Confidence Intervals for Quantiles
23 - Estimation of Distribution Functions and Quantiles
23.2 ESTIMATION OF DISTRIBUTION FUNCTIONS
23.2.1 Design-Based Estimation
23.2.2 Design-Based Estimators Using Auxiliary Information
23.2.3 Model-Based Estimators
23.2.4 Model-Assisted Estimators
23.2.5 Nonparametric Regression Method
23.2.5.1 Nandaraya-Watson Estimator
23.2.5.2 Breidt and Opsomer Estimator
23.2.6 Calibration Method
23.2.7 Method of Poststratification
23.2.8 Empirical Comparison of the Estimators
23.3 ESTIMATION OF QUANTILES
23.4 ESTIMATION OF MEDIAN
23.4.1 Position Estimator and Stratification Estimator
23.4.2 Comparison of the Efficiencies
23.4.3 Further Generalization
23.4.4 Empirical Comparison
23.5 CONFIDENCE INTERVAL FOR DISTRIBUTION FUNCTION AND QUANTILES
24.3 EXPERIMENTAL DESIGN CONFIGURATIONS
24.3.1 Equal Probability Sampling Design
24.3.2 Unequal Probability Sampling Design
24.3.3 Balanced Sampling Plan Without Contiguous Units
24.4 APPLICATION OF LINEAR PROGRAMMING
24.5 NEAREST PROPORTIONAL TO SIZE DESIGN
24.6 APPLICATION OF NONLINEAR PROGRAMMING
24.7 COORDINATION OF SAMPLES OVERTIME
24.7.2 Probability Proportional to Aggregate Size Sampling Scheme
25 - Empirical Likelihood Method in Survey Sampling
25.3 EMPIRICAL LIKELIHOOD APPROACH
25.4 EMPIRICAL LIKELIHOOD FOR SIMPLE RANDOM SAMPLING
25.5 PSEUDO–EMPIRICAL LIKELIHOOD METHOD
25.5.1 MPEL Estimator for the Population Mean
25.5.2 MPEL Estimator for the Population Distribution Function
25.5.3 MPEL Estimator Under Linear Constraints
25.6 ASYMPTOTIC BEHAVIOR OF MPEL ESTIMATOR
25.6.1 GREG Estimator Versus MPEL Estimator
25.7 EMPIRICAL LIKELIHOOD FOR STRATIFIED SAMPLING
25.7.1 Asymptotic Properties
25.7.1.1 Variance Estimation
25.7.1.2 Jackknife Variance Estimation
25.7.2 Pseudo–empirical Likelihood Estimator
25.7.2.1 Multistage Sampling
25.8 MODEL-CALIBRATED PSEUDOEMPIRICAL LIKELIHOOD
25.8.1 Estimation of the Population Mean
25.8.2 Estimation of the Population Distribution Function
25.8.3 Model-Calibrated MPEL Estimation for Population Quadratic Parameters
25.9 PSEUDO–EMPIRICAL LIKELIHOOD TO RAKING
25.10 EMPIRICAL LIKELIHOOD RATIO CONFIDENCE INTERVALS
25.10.1 Simple Random Sampling
25.10.2 Complex Sampling Designs
25.10.3 Stratified Sampling
25.10.4 Confidence Interval for Distribution Function
26 - Sampling Rare and Mobile Populations
26.2.1 Telephonic Interview
26.2.2 Mail Questionnaire
26.2.3.1 Sudman-Waksberg Method
26.2.4 Two-Phase Sampling
26.3 DISPROPORTIONATE SAMPLING
26.4 MULTIPLICITY OR NETWORK SAMPLING
26.5.1 Methods of Estimation
26.5.2 Simple Random Sampling Without Replacement
26.5.3 General Sampling Procedures
26.5.4 Horvitz-Thompson-Based Estimators
26.5.5 Concluding Remarks
26.9.1 Unbiased Estimation of Population Mean
26.9.1.1 Use of Intersection Probabilities
26.9.1.2 Use of the Number of Intersections
26.10 CAPTURE-RECAPTURE METHOD
26.10.1 Closed Population
26.10.1.1 Peterson and Lincoln Method
26.10.1.2 Hypergeometric Model
26.10.1.3 Bailey's Binomial Model
26.10.1.5 Inverse Sampling Methods
26.10.1.5.1 Without Replacement Method
26.10.1.5.2 With Replacement Method
26.10.1.6 Interval Estimation
26.10.1.7 Multiple Marking
26.10.2.1 Jolly-Seber Model
26.10.2.1.2 Assumptions of the Model
26.10.2.1.3 Estimation of Parameters
Survey Sampling Theory and Applications
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