Theory of sample surveys with R:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Konstanz
UVK-Verl.-Ges.
2015
München UVK/Lucius |
| Series: | UTB
4328 : Wirtschaftswissenschaften |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | 188 S. graph. Darst. 185 mm x 120 mm |
| ISBN: | 9783825243289 3825243281 |
Staff View
MARC
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Record in the Search Index
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| adam_text |
CONTENTS
LIST OF FIGURES 13
1 INTRODUCTION 15
1.1 SOURCES OF RANDOMNESS 16
1.1.1 STOCHASTIC MODEL 16
1.1.2 DESIGN APPROACH 17
1.2 SURVEYS 17
1.2.1 CHARACTERISTICS OF SURVEYS 17
1.2.2 SAMPLING FRAME 19
1.2.3 PROBABILITY SAMPLING 19
1.2.4 SAMPLING AND INFERENCE 19
1.3 SPECIFIC DESIGNS 20
1.3.1 SIMPLE RANDOM SAMPLING 20
1.3.2 STRATIFIED SAMPLING 20
1.3.3 CLUSTER SAMPLING . . 21
1.4 OUTLINE OF THE BOOK 21
1.5 EXERCISES 23
2 INTRODUCTION TO R 25
2.1 SOME R BASICS 26
2.1.1 OBJECT ORIENTATION 26
2.1.2 DATAFRAMES 26
2.1.3 SEQUENCES, REPLICATIONS, CONDITIONS
AND LOOPS 27
2.1.4 MATRICES 30
2.1.5 STORING AND READING DATA FILES 31
2.1.6 PROBABILITY DISTRIBUTIONS 32
2.1.7 GRAPHICS 33
2.1.8 LINEAR REGRESSION 34
2.2 SAMPLING FROM A POPULATION 36
2.2.1 ENUMERATION OF SAMPLES 36
2.2.2 THE SAMPLE() FUNCTION 37
2.3 EXERCISES 38
HTTP://D-NB.INFO/1061211851
8
CONTENTS
3 INCLUSION PROBABILITIES 41
3.1 INTRODUCTION 42
3.2 SOME NOTATION 42
3.3 INCLUSION INDICATOR I 43
3.4 A SMALL EXAMPLE 44
3.5 INCLUSION PROBABILITIES N 45
3.6 OBTAINING INCLUSION PROBABILITIES WITH R 46
3.7 SIMPLE RANDOM SAMPLING (SI) 47
3.8 PROPERTIES OF THE INCLUSION INDICATOR 50
3.8.1 THE EXPECTED VALUE OF THE INCLUSION
INDICATOR 51
3.8.2 THE VARIANCE OF THE INCLUSION INDICATOR . 51
3.8.3 THE COVARIANCE OF THE INCLUSION INDICATOR . . 51
3.8.4 PROPERTIES OF THE COVARIANCE 52
3.8.5 COVARIANCE MATRIX AND SUMS OF SUMS . 53
3.9 EXERCISES 54
4 ESTIMATION 57
4.1 INTRODUCTION 58
4.2 ESTIMATING FUNCTIONS AND ESTIMATORS 58
4.3 PROPERTIES OF ESTIMATION FUNCTIONS 58
4.4 THE 7R-ESTIMATOR 59
4.4.1 PROPERTIES OF THE 7R-ESTIMATOR 59
4.4.2 EXPECTED VALUE AND VARIANCE OF THE
7R-ESTIMATOR 59
4.4.3 AN ALTERNATIVE EXPRESSION OF THE VARIANCE . 62
4.4.4 THE YATES-GRUNDY VARIANCE OF THE TOTAL . . 62
4.5 ESTIMATION USING R 64
4.5.1 A SMALL NUMERICAL EXAMPLE 64
4.5.2 AN EMPIRICAL EXAMPLE: PSID 68
4.6 GENERATING SAMPLES WITH UNEQUAL INCLUSION PROBA
BILITIES 70
4.6.1 PROBABILITIES PROPORTIONAL TO SIZE (PPS) . . 70
4.6.2 THE SAMPFORD-ALGORITHM 72
4.7 EXERCISES 73
5 SIMPLE SAMPLING 75
5.1 INTRODUCTION 76
5.2 SOME GENERAL ESTIMATION FUNCTIONS 76
5.2.1 THE 7R-ESTIMATOR FOR THE TOTAL 76
5.2.2 THE 7R-ESTIMATOR FOR THE MEAN 76
5.2.3 THE 7R-ESTIMATOR FOR A PROPORTION 77
CONTENTS 9
5.3 SIMPLE RANDOM SAMPLING 77
5.3.1 THE 7R-ESTIMATOR FOR THE TOTAL (SI) 78
5.3.2 THE 7R-ESTIMATOR FOR THE MEAN (SI) 79
5.3.3 THE 7R-ESTIMATOR FOR A PROPORTION (SI) . 80
5.4 SOME EXAMPLES USING R 81
5.5 EXERCISES 86
6 CONFIDENCE INTERVALS 89
6.1 INTRODUCTION 90
6.2 CHEBYSHEV-INEQUALITY 92
6.2.1 DERIVATION OF THE CHEBYSHEV-INEQUALITY . 92
6.2.2 APPLICATION OF THE CHEBYSHEV-
INEQUALITY 94
6.3 CONFIDENCE INTERVALS BASED ON A SPECIFIC SAMPLE . . 94
6.4 SOME GENERAL REMARKS 97
6.4.1 NO APPROXIMATE NORMALITY 97
6.4.2 SIMPLIFIED VARIANCE ESTIMATORS 97
6.4.3 EFFECT OF SIMPLIFICATION IN THE SIMPLE RANDOM
SAMPLING CASE 98
6.4.4 EFFECT OF SIMPLIFICATION FOR THE GENERAL
TT
-
ESTIMATOR 99
6.4.5 EFFECT OF SIMPLIFICATION IN STRATIFIED AND CLUS
TERED SAMPLES 99
6.4.6 BOOTSTRAP 100
6.5 EXERCISES 101
7 STRATIFIED SAMPLING 103
7.1 INTRODUCTION 104
7.2 SOME NOTATION AND AN EXAMPLE 104
7.2.1 NOTATION 104
7.2.2 EXAMPLE: SECTORS OF EMPLOYMENT AS STRATA . 105
7.3 ESTIMATION OF THE TOTAL 108
7.3.1 SIMPLE RANDOM SAMPLING WITHIN STRATA . . . 108
7.3.2 EXAMPLE: SIMPLE RANDOM SAMPLING WITHIN
SECTORS 110
7.4 CHOOSING THE SAMPLE SIZE FOR INDIVIDUAL STRATA . 110
7.4.1 THE MINIMIZATION PROBLEM ILL
7.4.2 THE CAUCHY-SCHWARZ INEQUALITY 112
7.4.3 SOLVING THE MINIMIZATION PROBLEM 113
7.4.4 EXAMPLE: OPTIMAL SAMPLING SIZE WITHIN
SECTORS 115
10
CONTENTS
7.5 SAMPLE ALLOCATION AND EFFICIENCY 116
7.5.1 VARIANCE COMPARISONS BASED ON THE VARIANCE
DECOMPOSITION 117
7.5.2 NO STRATIFICATION VERSUS PROPORTIONAL
ALLOCATION 118
7.5.3 PROPORTIONAL ALLOCATION VERSUS OPTIMAL ALLO
CATION 118
7.5.4 NO STRATIFICATION VERSUS OPTIMAL ALLOCATION . 119
7.5.5 AN EFFICIENCY COMPARISON WITH FT 120
7.6 EXERCISES 123
8 CLUSTER SAMPLING 125
8.1 INTRODUCTION 126
8.2 NOTATION 126
8.2.1 CLUSTERING THE POPULATION 126
8.2.2 ARTIFICIALLY CLUSTERING THE PSID SAMPLE . . . 127
8.2.3 SAMPLING CLUSTERS 127
8.2.4 INCLUSION PROBABILITIES 128
8.3 ESTIMATING THE POPULATION TOTAL 129
8.3.1 THE 7R-ESTIMATOR OF THE POPULATION TOTAL . . 129
8.3.2 VARIANCE OF THE 7R-ESTIMATOR OF THE POPULATION
TOTAL 130
8.4 SIMPLE RANDOM SAMPLING OF CLUSTERS (SIC) 131
8.4.1 THE 7R-ESTIMATOR OF THE POPULATION TOTAL . . 131
8.4.2 THE 7R-ESTIMATOR IN THE PSID EXAMPLE . . . 131
8.4.3 VARIANCE OF THE 7R-ESTIMATOR OF THE POPULATION
TOTAL 132
8.4.4 VARIANCE OF THE MEAN ESTIMATOR IN THE PSID
EXAMPLE 133
8.5 EXERCISES 135
9 AUXILIARY VARIABLES 137
9.1 INTRODUCTION 138
9.2 THE RATIO ESTIMATOR 139
9.2.1 EXAMPLE OF THE RATIO ESTIMATOR USING PSID
DATA 140
9.2.2 TAYLOR SERIES EXPANSION 142
9.2.3 THE APPROXIMATE VARIANCE OF THE RATIO ESTI
MATOR 145
9.2.4 ESTIMATING THE APPROXIMATE VARIANCE OF THE
RATIO ESTIMATOR USING PSID DATA 146
CONTENTS
11
9.2.5 COMPARISON OF THE RATIO ESTIMATOR WITH THE
SIMPLE 7R-ESTIMATOR 148
9.2.6 THE RATIO ESTIMATOR IN THE REGRESSION
CONTEXT 149
9.2.7 THE LINEAR REGRESSION MODEL UNDER SPECIFIC
HETEROSKEDASTICITY ASSUMPTION 151
9.3 THE DIFFERENCE ESTIMATOR 152
9.3.1 THE DIFFERENCE ESTIMATOR USING REGRESSION
NOTATION 152
9.3.2 PROPERTIES OF THE DIFFERENCE ESTIMATOR . 153
9.3.3 THE DIFFERENCE ESTIMATOR OF AVERAGE WAGE
USING THE PSID DATA 154
9.4 EXERCISES 158
10 REGRESSION 161
10.1 INTRODUCTION 162
10.1.1 REGRESSION WITHOUT INTERCEPT 162
10.1.2 REGRESSION WITH INTERCEPT 165
10.1.3 MULTIVARIATE LINEAR REGRESSION WITH INTERCEPT 167
10.2 VARIANCE OF THE PARAMETER ESTIMATORS 169
10.2.1 LINEAR APPROXIMATION OF THE
7R-ESTIMATOR 169
10.2.2 THE VARIANCE OF THE LINEAR APPROXIMATION OF
THE 7R-ESTIMATOR 171
10.2.3 SIMPLE REGRESSION THROUGH THE ORIGIN . 175
10.2.4 SIMPLE REGRESSION WITH INTERCEPT 176
10.2.5 SIMPLE REGRESSION WITH INTERCEPT AND SIMPLE
RANDOM SAMPLING 177
10.2.6 WAGE REGRESSION WITH PSID DATA AND SIMPLE
RANDOM SAMPLING 177
10.3 EXERCISES 180
INDICES 183
FUNCTIONS INDEX 183
SUBJECT INDEX 185 |
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| dewey-ones | 330 - Economics |
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| dewey-search | 330.015195 |
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| dewey-tens | 330 - Economics |
| discipline | Informatik Mathematik Wirtschaftswissenschaften |
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| indexdate | 2024-08-03T02:15:23Z |
| institution | BVB |
| isbn | 9783825243289 3825243281 |
| language | English |
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| physical | 188 S. graph. Darst. 185 mm x 120 mm |
| publishDate | 2015 |
| publishDateSearch | 2015 |
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| spelling | Behr, Andreas 1967- Verfasser (DE-588)133124029 aut Theory of sample surveys with R Andreas Behr Konstanz UVK-Verl.-Ges. 2015 München UVK/Lucius 188 S. graph. Darst. 185 mm x 120 mm txt rdacontent n rdamedia nc rdacarrier UTB 4328 : Wirtschaftswissenschaften R Programm (DE-588)4705956-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content R Programm (DE-588)4705956-4 s Statistik (DE-588)4056995-0 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4831103&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027875903&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Behr, Andreas 1967- Theory of sample surveys with R R Programm (DE-588)4705956-4 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4705956-4 (DE-588)4056995-0 (DE-588)4123623-3 |
| title | Theory of sample surveys with R |
| title_auth | Theory of sample surveys with R |
| title_exact_search | Theory of sample surveys with R |
| title_full | Theory of sample surveys with R Andreas Behr |
| title_fullStr | Theory of sample surveys with R Andreas Behr |
| title_full_unstemmed | Theory of sample surveys with R Andreas Behr |
| title_short | Theory of sample surveys with R |
| title_sort | theory of sample surveys with r |
| topic | R Programm (DE-588)4705956-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | R Programm Statistik Lehrbuch |
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