Sampling and Estimation from Finite Populations - Yves Tille

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15: Variance Estimation by Linearization 15.1 Introduction 15.2 Orders of Magnitude in Probability 15.3 Asymptotic Hypotheses 15.4 Linearization of Functions of Interest 15.5 Linearization by Steps 15.6 Linearization of an Implicit Function of Interest 15.7 Influence Function Approach 15.8 Binder's Cookbook Approach 15.9 Demnati and Rao Approach 15.10 Linearization by the Sample Indicator Variables 15.11 Discussion on Variance Estimation

      23  Chapter 16: Treatment of Nonresponse 16.1 Sources of Error 16.2 Coverage Errors 16.3 Different Types of Nonresponse 16.4 Nonresponse Modeling 16.5 Treating Nonresponse by Reweighting 16.6 Imputation 16.7 Variance Estimation with Nonresponse

      24  Chapter 17: Summary Solutions to the Exercises

      25  Bibliography

      26  Author Index

      27  Subject Index

      28  End User License Agreement

      List of Tables

      1 Chapter 3Table 3.1 Simple designs: summary table.Table 3.2 Example of sample sizes required for different population sizes and di...

      2 Chapter 4Table 4.1 Application of optimal allocation: the sample size is larger than the ...Table 4.2 Second application of optimal allocation in strata 1 and 2.

      3 Chapter 5Table 5.1 Minimum support design.Table 5.2 Decomposition into simple random sampling designs.Table 5.3 Decomposition into

simple random sampling designs. Table 5.4 Properties of the methods.

      4 Chapter 6Table 6.1 Population of 20 students with variables, constant, gender (1, male, 2...Table 6.2 Totals and expansion estimators for balancing variables.Table 6.3 Variances of the expansion estimators of the means under simple random...

      5 Chapter 7Table 7.1 Block number, number of households, and total household income.

      6 Chapter 8Table 8.1 Means of spatial balancing measures based on Voronoï polygons

and mod...Table 8.2 Selection intervals for negative coordination and selection indicators...Table 8.3 Selection indicators for each selection interval for unit
.

      7 Chapter 9Table 9.1 Estimation methods: summary table.

      8 Chapter 10Table 10.1 Population partition.Table 10.2 Totals with respect to two variables.Table 10.3 Calibration, starting table.Table 10.4 Salaries in Euros.Table 10.5 Estimated totals using simple random sampling without replacement.Table 10.6 Known margins using a census.Table 10.7 Iteration 1: row total adjustment.Table 10.8 Iteration 2: column total adjustment.Table 10.9 Iteration 3: row total adjustment.Table 10.10 Iteration 4: column total adjustment.Table 1Table 2

      9 Chapter 12Table 12.1 Pseudo‐distances for calibration.Table 12.2 Calibration functions and their derivatives.Table 12.3 Minima, maxima, means, and standard deviations of the weights for eac...

      10 Chapter 14Table 14.1 Sample, variable of interest

, weights
, cumulative weights
and re...Table 14.2 Table of fictitious incomes
, weights
, cumulative weights
, relati...Table 14.3 Totals necessary to estimate the Gini index.

      11 Chapter 17Table 1Table 2

      List of Illustrations

      1 Chapter 1Figure 1.1 Auxiliary information can be used before or after data collection t...

      2 Chapter 4Figure 4.1 Stratified design: the samples are selected independently from one ...

      3 Chapter 5Figure 5.1 Systematic sampling: example with inclusion probabilities

Figure 5.2 Method of Deville.Figure 5.3 Splitting into two parts.Figure 5.4 Splitting in
parts.Figure 5.5 Minimum support design.Figure 5.6 Decomposition into simple random sampling designs.Figure 5.7 Pivotal method applied on vector
.

      4 Chapter 6Figure 6.1 Possible samples in a population of size

3.Figure 6.2 Fixed size constraint: the three samples of size
2 are connected ...Figure 6.3 None of the vertices of
is a vertex of the cube.Figure 6.4 Two vertices of
are vertices of the cube, but the third is not.Figure 6.5 Flight phase in a population of size
3 with a constraint of fixed...

      5 Chapter 7Figure 7.1 Cluster sampling: the population is divided into clusters. Clusters...Figure

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