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E-grāmata: Sampling and Estimation from Finite Populations

(Universite de Neuchatel)
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Sampling and Estimation from Finite PopulationsPalielināt
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This 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.

A much-needed reference on survey sampling and its applications that presents the latest advances in the field

Seeking to show that sampling theory is a living discipline with a very broad scope, this book examines the modern development of the theory of survey sampling and the foundations of survey sampling. It offers readers a critical approach to the subject and discusses putting theory into practice. It also explores the treatment of non-sampling errors featuring a range of topics from the problems of coverage to the treatment of non-response. In addition, the book includes real examples, applications, and a large set of exercises with solutions.

Sampling and Estimation from Finite Populations begins with a look at the history of survey sampling. It then offers chapters on: population, sample, and estimation; simple and systematic designs; stratification; sampling with unequal probabilities; balanced sampling; cluster and two-stage sampling; and other topics on sampling, such as spatial sampling, coordination in repeated surveys, and multiple survey frames. The book also includes sections on: post-stratification and calibration on marginal totals; calibration estimation; estimation of complex parameters; variance estimation by linearization; and much more.

  • Provides an up-to-date review of the theory of sampling
  • Discusses the foundation of inference in survey sampling, in particular, the model-based and design-based frameworks
  • Reviews the problems of application of the theory into practice
  • Also deals with the treatment of non sampling errors

Sampling and Estimation from Finite Populations is an excellent book for methodologists and researchers in survey agencies and advanced undergraduate and graduate students in social science, statistics, and survey courses.

Recenzijas

"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 aheadboth foreseen and yet to be identified." Carl M. O'Brien, Lowestoft Laboratory, International Statistical Review (2020) doi:10.1111/insr.12420

List of Figures
xiii
List of Tables
xvii
List of Algorithms
xix
Preface xxi
Preface to the First French Edition xxiii
Table of Notations
xxv
1 A History of Ideas in Survey Sampling Theory
1(12)
1.1 Introduction
1(1)
1.2 Enumerative Statistics During the 19th Century
2(2)
1.3 Controversy on the use of Partial Data
4(1)
1.4 Development of a Survey Sampling Theory
5(1)
1.5 The US Elections of 1936
6(1)
1.6 The Statistical Theory of Survey Sampling
6(2)
1.7 Modeling the Population
8(1)
1.8 Attempt to a Synthesis
9(1)
1.9 Auxiliary Information
9(1)
1.10 Recent References and Development
10(3)
2 Population, Sample, and Estimation
13(14)
2.1 Population
13(1)
2.2 Sample
14(1)
2.3 Inclusion Probabilities
15(2)
2.4 Parameter Estimation
17(1)
2.5 Estimation of a Total
18(1)
2.6 Estimation of a Mean
19(1)
2.7 Variance of the Total Estimator
20(2)
2.8 Sampling with Replacement
22(5)
Exercises
24(3)
3 Simple and Systematic Designs
27(38)
3.1 Simple Random Sampling without Replacement with Fixed Sample Size
27(5)
3.1.1 Sampling Design and Inclusion Probabilities
27(1)
3.1.2 The Expansion Estimator and its Variance
28(3)
3.1.3 Comment on the Variance-Covariance Matrix
31(1)
3.2 Bernoulli Sampling
32(4)
3.2.1 Sampling Design and Inclusion Probabilities
32(2)
3.2.2 Estimation
34(2)
3.3 Simple Random Sampling with Replacement
36(2)
3.4 Comparison of the Designs with and Without Replacement
38(1)
3.5 Sampling with Replacement and Retaining Distinct Units
38(7)
3.5.1 Sample Size and Sampling Design
38(3)
3.5.2 Inclusion Probabilities and Estimation
41(3)
3.5.3 Comparison of the Estimators
44(1)
3.6 Inverse Sampling with Replacement
45(2)
3.7 Estimation of Other Functions of Interest
47(3)
3.7.1 Estimation of a Count or a Proportion
47(1)
3.7.2 Estimation of a Ratio
48(2)
3.8 Determination of the Sample Size
50(1)
3.9 Implementation of Simple Random Sampling Designs
51(6)
3.9.1 Objectives and Principles
51(1)
3.9.2 Bernoulli Sampling
51(1)
3.9.3 Successive Drawing of the Units
52(1)
3.9.4 Random Sorting Method
52(1)
3.9.5 Selection-Rejection Method
53(1)
3.9.6 The Reservoir Method
54(2)
3.9.7 Implementation of Simple Random Sampling with Replacement
56(1)
3.10 Systematic Sampling with Equal Probabilities
57(1)
3.11 Entropy for Simple and Systematic Designs
58(7)
3.11.1 Bernoulli Designs and Entropy
58(2)
3.11.2 Entropy and Simple Random Sampling
60(1)
3.11.3 General Remarks
61(1)
Exercises
61(4)
4 Stratification
65(18)
4.1 Population and Strata
65(1)
4.2 Sample, Inclusion Probabilities, and Estimation
66(2)
4.3 Simple Stratified Designs
68(2)
4.4 Stratified Design with Proportional Allocation
70(1)
4.5 Optimal Stratified Design for the Total
71(3)
4.6 Notes About Optimality in Stratification
74(1)
4.7 Power Allocation
75(1)
4.8 Optimality and Cost
76(1)
4.9 Smallest Sample Size
76(1)
4.10 Construction of the Strata
77(2)
4.10.1 General Comments
77(1)
4.10.2 Dividing a Quantitative Variable in Strata
77(2)
4.11 Stratification Under Many Objectives
79(4)
Exercises
80(3)
5 Sampling with Unequal Probabilities
83(36)
5.1 Auxiliary Variables and Inclusion Probabilities
83(1)
5.2 Calculation of the Inclusion Probabilities
84(1)
5.3 General Remarks
85(1)
5.4 Sampling with Replacement with Unequal Inclusion Probabilities
86(2)
5.5 Nonvalidity of the Generalization of the Successive Drawing without Replacement
88(1)
5.6 Systematic Sampling with Unequal Probabilities
89(2)
5.7 Deville's Systematic Sampling
91(1)
5.8 Poisson Sampling
92(3)
5.9 Maximum Entropy Design
95(3)
5.10 Rao-Sampford Rejective Procedure
98(2)
5.11 Order Sampling
100(1)
5.12 Splitting Method
101(9)
5.12.1 General Principles
101(2)
5.12.2 Minimum Support Design
103(1)
5.12.3 Decomposition into Simple Random Sampling Designs
104(3)
5.12.4 Pivotal Method
107(2)
5.12.5 Brewer Method
109(1)
5.13 Choice of Method
110(1)
5.14 Variance Approximation
111(3)
5.15 Variance Estimation
114(5)
Exercises
115(4)
6 Balanced Sampling
119(24)
6.1 Introduction
119(1)
6.2 Balanced Sampling: Definition
120(2)
6.3 Balanced Sampling and Linear Programming
122(1)
6.4 Balanced Sampling by Systematic Sampling
123(1)
6.5 Methode of Deville, Grosbras, and Roth
124(1)
6.6 Cube Method
125(12)
6.6.1 Representation of a Sampling Design in the form of a Cube
125(1)
6.6.2 Constraint Subspace
126(1)
6.6.3 Representation of the Rounding Problem
127(3)
6.6.4 Principle of the Cube Method
130(1)
6.6.5 The Flight Phase
130(3)
6.6.6 Landing Phase by Linear Programming
133(1)
6.6.7 Choice of the Cost Function
134(1)
6.6.8 Landing Phase by Relaxing Variables
135(1)
6.6.9 Quality of Balancing
135(1)
6.6.10 An Example
136(1)
6.7 Variance Approximation
137(3)
6.8 Variance Estimation
140(1)
6.9 Special Cases of Balanced Sampling
141(1)
6.10 Practical Aspects of Balanced Sampling
141(2)
Exercise
142(1)
7 Cluster and Two-stage Sampling
143(24)
7.1 Cluster Sampling
143(5)
7.1.1 Notation and Definitions
143(3)
7.1.2 Cluster Sampling with Equal Probabilities
146(1)
7.1.3 Sampling Proportional to Size
147(1)
7.2 Two-stage Sampling
148(9)
7.2.1 Population, Primary, and Secondary Units
149(2)
7.2.2 The Expansion Estimator and its Variance
151(4)
7.2.3 Sampling with Equal Probability
155(1)
7.2.4 Self-weighting Two-stage Design
156(1)
7.3 Multi-stage Designs
157(1)
7.4 Selecting Primary Units with Replacement
158(3)
7.5 Two-phase Designs
161(2)
7.5.1 Design and Estimation
161(1)
7.5.2 Variance and Variance Estimation
162(1)
7.6 Intersection of Two Independent Samples
163(4)
Exercises
165(2)
8 Other Topics on Sampling
167(28)
8.1 Spatial Sampling
167(5)
8.1.1 The Problem
167(1)
8.1.2 Generalized Random Tessellation Stratified Sampling
167(2)
8.1.3 Using the Traveling Salesman Method
169(1)
8.1.4 The Local Pivotal Method
169(1)
8.1.5 The Local Cube Method
169(1)
8.1.6 Measures of Spread
170(2)
8.2 Coordination in Repeated Surveys
172(10)
8.2.1 The Problem
172(1)
8.2.2 Population, Sample, and Sample Design
173(1)
8.2.3 Sample Coordination and Response Burden
174(1)
8.2.4 Poisson Method with Permanent Random Numbers
175(1)
8.2.5 Kish and Scott Method for Stratified Samples
176(1)
8.2.6 The Cotton and Hesse Method
176(1)
8.2.7 The Riviere Method
177(1)
8.2.8 The Netherlands Method
178(1)
8.2.9 The Swiss Method
178(3)
8.2.10 Coordinating Unequal Probability Designs with Fixed Size
181(1)
8.2.11 Remarks
181(1)
8.3 Multiple Survey Frames
182(5)
8.3.1 Introduction
182(1)
8.3.2 Calculating Inclusion Probabilities
183(1)
8.3.3 Using Inclusion Probability Sums
184(1)
8.3.4 Using a Multiplicity Variable
185(1)
8.3.5 Using a Weighted Multiplicity Variable
186(1)
8.3.6 Remarks
187(1)
8.4 Indirect Sampling
187(4)
8.4.1 Introduction
187(1)
8.4.2 Adaptive Sampling
188(1)
8.4.3 Snowball Sampling
188(1)
8.4.4 Indirect Sampling
189(1)
8.4.5 The Generalized Weight Sharing Method
190(1)
8.5 Capture--Recapture
191(4)
9 Estimation with a Quantitative Auxiliary Variable
195(14)
9.1 The Problem
195(1)
9.2 Ratio Estimator
196(5)
9.2.1 Motivation and Definition
196(1)
9.2.2 Approximate Bias of the Ratio Estimator
197(1)
9.2.3 Approximate Variance of the Ratio Estimator
198(1)
9.2.4 Bias Ratio
199(1)
9.2.5 Ratio and Stratified Designs
199(2)
9.3 The Difference Estimator
201(1)
9.4 Estimation by Regression
202(2)
9.5 The Optimal Regression Estimator
204(1)
9.6 Discussion of the Three Estimation Methods
205(4)
Exercises
208(1)
10 Post-Stratification and Calibration on Marginal Totals
209(16)
10.1 Introduction
209(1)
10.2 Post-Stratification
209(3)
10.2.1 Notation and Definitions
209(2)
10.2.2 Post-Stratified Estimator
211(1)
10.3 The Post-Stratified Estimator in Simple Designs
212(5)
10.3.1 Estimator
212(1)
10.3.2 Conditioning in a Simple Design
213(1)
10.3.3 Properties of the Estimator in a Simple Design
214(3)
10.4 Estimation by Calibration on Marginal Totals
217(4)
10.4.1 The Problem
217(1)
10.4.2 Calibration on Marginal Totals
218(2)
10.4.3 Calibration and Kullback--Leibler Divergence
220(1)
10.4.4 Raking Ratio Estimation
221(1)
10.5 Example
221(4)
Exercises
224(1)
11 Multiple Regression Estimation
225(12)
11.1 Introduction
225(1)
11.2 Multiple Regression Estimator
226(1)
11.3 Alternative Forms of the Estimator
227(2)
11.3.1 Homogeneous Linear Estimator
227(1)
11.3.2 Projective Form
228(1)
11.3.3 Cosmetic Form
228(1)
11.4 Calibration of the Multiple Regression Estimator
229(1)
11.5 Variance of the Multiple Regression Estimator
230(1)
11.6 Choice of Weights
231(1)
11.7 Special Cases
231(5)
11.7.1 Ratio Estimator
231(1)
11.7.2 Post-stratified Estimator
231(2)
11.7.3 Regression Estimation with a Single Explanatory Variable
233(1)
11.7.4 Optimal Regression Estimator
233(2)
11.7.5 Conditional Estimation
235(1)
11.8 Extension to Regression Estimation
236(1)
Exercise
236(1)
12 Calibration Estimation
237(26)
12.1 Calibrated Methods
237(2)
12.2 Distances and Calibration Functions
239(13)
12.2.1 The Linear Method
239(1)
12.2.2 The Raking Ratio Method
240(2)
12.2.3 Pseudo Empirical Likelihood
242(2)
12.2.4 Reverse Information
244(1)
12.2.5 The Truncated Linear Method
245(1)
12.2.6 General Pseudo-Distance
246(3)
12.2.7 The Logistic Method
249(1)
12.2.8 Deville Calibration Function
249(2)
12.2.9 Roy and Vanheuverzwyn Method
251(1)
12.3 Solving Calibration Equations
252(3)
12.3.1 Solving by Newton's Method
252(1)
12.3.2 Bound Management
253(1)
12.3.3 Improper Calibration Functions
254(1)
12.3.4 Existence of a Solution
254(1)
12.4 Calibrating on Households and Individuals
255(1)
12.5 Generalized Calibration
256(2)
12.5.1 Calibration Equations
256(1)
12.5.2 Linear Calibration Functions
257(1)
12.6 Calibration in Practice
258(1)
12.7 An Example
259(4)
Exercises
260(3)
13 Model-Based approach
263(18)
13.1 Model Approach
263(1)
13.2 The Model
263(4)
13.3 Homoscedastic Constant Model
267(1)
13.4 Heteroscedastic Model 1 Without Intercept
267(2)
13.5 Heteroscedastic Model 2 Without Intercept
269(1)
13.6 Univariate Homoscedastic Linear Model
270(1)
13.7 Stratified Population
271(2)
13.8 Simplified Versions of the Optimal Estimator
273(3)
13.9 Completed Heteroscedasticity Model
276(1)
13.10 Discussion
277(1)
13.11 An Approach that is Both Model- and Design-based
277(4)
14 Estimation of Complex Parameters
281(14)
14.1 Estimation of a Function of Totals
281(1)
14.2 Variance Estimation
282(1)
14.3 Covariance Estimation
283(1)
14.4 Implicit Function Estimation
283(1)
14.5 Cumulative Distribution Function and Quantiles
284(4)
14.5.1 Cumulative Distribution Function Estimation
284(1)
14.5.2 Quantile Estimation: Method 1
284(1)
14.5.3 Quantile Estimation: Method 2
285(2)
14.5.4 Quantile Estimation: Method 3
287(1)
14.5.5 Quantile Estimation: Method 4
288(1)
14.6 Cumulative Income, Lorenz Curve, and Quintile Share Ratio
288(2)
14.6.1 Cumulative Income Estimation
288(1)
14.6.2 Lorenz Curve Estimation
289(1)
14.6.3 Quintile Share Ratio Estimation
289(1)
14.7 Gini Index
290(1)
14.8 An Example
291(4)
15 Variance Estimation by Linearization
295(38)
15.1 Introduction
295(1)
15.2 Orders of Magnitude in Probability
295(5)
15.3 Asymptotic Hypotheses
300(3)
15.3.1 Linearizing a Function of Totals
301(2)
15.3.2 Variance Estimation
303(1)
15.4 Linearization of Functions of Interest
303(5)
15.4.1 Linearization of a Ratio
303(1)
15.4.2 Linearization of a Ratio Estimator
304(1)
15.4.3 Linearization of a Geometric Mean
305(1)
15.4.4 Linearization of a Variance
305(1)
15.4.5 Linearization of a Covariance
306(1)
15.4.6 Linearization of a Vector of Regression Coefficients
307(1)
15.5 Linearization by Steps
308(2)
15.5.1 Decomposition of Linearization by Steps
308(1)
15.5.2 Linearization of a Regression Coefficient
308(1)
15.5.3 Linearization of a Univariate Regression Estimator
309(1)
15.5.4 Linearization of a Multiple Regression Estimator
309(1)
15.6 Linearization of an Implicit Function of Interest
310(4)
15.6.1 Estimating Equation and Implicit Function of Interest
310(1)
15.6.2 Linearization of a Logistic Regression Coefficient
311(2)
15.6.3 Linearization of a Calibration Equation Parameter
313(1)
15.6.4 Linearization of a Calibrated Estimator
313(1)
15.7 Influence Function Approach
314(7)
15.7.1 Function of Interest, Functional
314(1)
15.7.2 Definition
315(1)
15.7.3 Linearization of a Total
316(1)
15.7.4 Linearization of a Function of Totals
316(1)
15.7.5 Linearization of Sums and Products
317(1)
15.7.6 Linearization by Steps
318(1)
15.7.7 Linearization of a Parameter Defined by an Implicit Function
318(1)
15.7.8 Linearization of a Double Sum
319(2)
15.8 Binder's Cookbook Approach
321(1)
15.9 Demnati and Rao Approach
322(2)
15.10 Linearization by the Sample Indicator Variables
324(7)
15.10.1 The Method
324(2)
15.10.2 Linearization of a Quantile
326(1)
15.10.3 Linearization of a Calibrated Estimator
327(1)
15.10.4 Linearization of a Multiple Regression Estimator
328(1)
15.10.5 Linearization of an Estimator of a Complex Function with Calibrated Weights
329(1)
15.10.6 Linearization of the Gini Index
330(1)
15.11 Discussion on Variance Estimation
331(2)
Exercises
331(2)
16 Treatment of Nonresponse
333(26)
16.1 Sources of Error
333(1)
16.2 Coverage Errors
334(1)
16.3 Different Types of Nonresponse
334(1)
16.4 Nonresponse Modeling
335(1)
16.5 Treating Nonresponse by Reweighting
336(6)
16.5.1 Nonresponse Coming from a Sample
336(1)
16.5.2 Modeling the Nonresponse Mechanism
337(2)
16.5.3 Direct Calibration of Nonresponse
339(2)
16.5.4 Reweighting by Generalized Calibration
341(1)
16.6 Imputation
342(5)
16.6.1 General Principles
342(1)
16.6.2 Imputing From an Existing Value
342(1)
16.6.3 Imputation by Prediction
342(1)
16.6.4 Link Between Regression Imputation and Reweighting
343(2)
16.6.5 Random Imputation
345(2)
16.7 Variance Estimation with Nonresponse
347(12)
16.7.1 General Principles
347(1)
16.7.2 Estimation by Direct Calibration
348(1)
16.7.3 General Case
349(1)
16.7.4 Variance for Maximum Likelihood Estimation
350(3)
16.7.5 Variance for Estimation by Calibration
353(3)
16.7.6 Variance of an Estimator Imputed by Regression
356(1)
16.7.7 Other Variance Estimation Techniques
357(2)
17 Summary Solutions to the Exercises
359(20)
Bibliography 379(26)
Author Index 405(6)
Subject Index 411
YVES TILLÉ, PhD, is a Professor at the University of Neuchātel (Université de Neuchātel) in Neuchātel, Switzerland.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
Permanent link: https://www.kriso.lv/db/97811190712662e.html
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