A concise introduction to statistical inference:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton
CRC Press, Taylor and Francis Group
[2017]
|
| Series: | A> Chapman & Hall Book
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xix, 210 Seiten Diagramme |
| ISBN: | 9781498755771 9781498755962 |
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MARC
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Record in the Search Index
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| adam_text | Contents
List of Figures xi
Preface xiii
Acknowledgments xix
1 Statistical Inference 1
1.1 What statistical inference is all about........................ 1
1.2 Why statistical inference is difficult . . . .................. 2
1.3 What kind of parameters are we interested in? ................. 3
1.3.1 Center of a distribution................................ 4
1.3.2 Spread of a distribution.............................. 5
1.3.3 Association between variables........................... 6
1.4 Statistics and probability ................................... 8
1.5 Chapter summary................................................ 9
2 Theory and Calculus of Probability 11
2.1 Probability models ........................................... 11
2.2 Random variables and their distributions................ . 15
2.3 Moments of random variables .................................. 19
2.3.1 Expectation............................................ 19
2.3.2 Higher order moments................................... 21
2.3.3 Variance.............................................. 22
2.4 Multivariate distributions ................................... 23
2.4.1 Association between two random variables............... 24
2.5 Normal distribution........................................... 25
2.5.1 Bivariate normal distribution.......................... 27
2.6 Limit theorems for the sample mean . .................. 28
2.7 Chapter summary............................................... 32
2.8 Exercises and problems...................................... 32 3
3 From Probability to Statistics 39
3.1 A first stab at statistical inference......................... 40
3.2 Sampling distributions ....................................... 42
3.3 Chapter summary............................................... 43
3.4 Exercises and problems ....................................... 44
vii
viii Contents
4 Statistical Inference for the Mean based on a Large Sample 47
4.1 Simple statistical model for the mean ........................ 47
4.2 Confidence intervals . f...................................... 49
4.3 Hypothesis tests.............................................. 51
4.3.1 The p-value......................................... 52
4.3.2 Errors and power....................................... 54
4.4 Chapter summary.............................................. 57
4.5 Exercises and problems........................................ 57
5 Statistical Models and Sampling Distributions 61
5.1 Statistical models........................................... 61
5.2 Some examples of statistical models........................... 64
5.3 Statistics.................................................... 65
5.4 Sampling distributions ...................................... 68
5.5 Chapter summary............................................. 72
5.6 Exercises and problems........................................ 72
6 Estimation of Parameters 77
6.1 Introduction.................................................. 77
6.2 Maximum likelihood estimators ................................ 77
6.3 Comparing estimators ......................................... 82
6.3.1 Unbiased estimators.................................... 82
6.3.2 Mean squared error .................................... 86
6.4 Method of moments............................................. 90
6.5 A useful asymptotic result ................................. 92
6.6 Chapter summary.............................................. 93
6.7 Exercises and problems.................................. 94 7 * *
7 Confidence Intervals 99
7.1 Introduction................................................ 99
7.2 Basic idea ................................................... 99
7.3 Confidence intervals for means............................... 102
7.3.1 Mean of a normal population with variance known . . 102
7.3.2 Mean of a normal population with variance unknown 103
7.3.3 Mean of an unknown distribution based on a large sam-
ple ......................................................... 104
7.4 Confidence interval for any parameter based on a large sample 105
7.5 Differences between populations based on large samples . . 106
7.5.1 Difference between population means . . .............. 106
7.5.2 Difference between proportions........................ 107
7.6 Confidence intervals for the variance of a normal sample . . 108
7.7 Chapter summary............................................. 110
7.8 Exercises and problems....................................... 110
Contents ix
8 Hypothesis Testing 117
8.1 Introduction................................................ 117
8.2 Hypotheses, decisions, and errors .......................... 117
8.3 What test statistic should we use? ......................... 122
8.4 Examples of commonly used tests............................. 126
8.4.1 Test of a normal mean with known variance............ 127
8.4.2 Test of a normal mean with unknown variance .... 128
8.4.3 Test of a mean based on a large sample............... 130
8.4.4 Test of a proportion based on a large sample......... 130
8.4.5 Test of the difference between two means based on a
large sample........................................ 131
8.4.6 Test of the difference between two proportions in a large
sample............................................... 132
8.5 p-value..................................................... 133
8.6 Statistical significance ................................... 134
8.7 Chapter summary............................................ 136
8.8 Exercises, problems, and discussion......................... 137
9 Linear Regression 145
9.1 Basic ideas ................................................ 145
9.2 Estimation: Least squares method............................ 148
9.3 Decomposition of errors .................................... 150
9.4 Inferences based on the OLS estimator . .................... 151
9.5 Linear regression, causation, and correlation............... 153
9.6 Chapter summary ............................................ 154
9.7 Exercises, problems, and discussion...................... 155 10
10 Bayesian Inference 161
10.1 Introduction............................................... 161
10.2 Basic concepts............................................. 162
10.3 A simple statistical model from a Bayesian perspective ... 164
10.4 Highest density regions.................................... 166
10.5 Hypothesis testing ........................................ 167
10.6 Evidence and the likelihood principle...................... 170
10.7 Decision theory ........................................... 173
10.8 An economic decision problem with statistical information . 177
10.9 Linear regression ......................................... 179
10.10 Chapter summary............................................ 180
10.11 Exercises and problems..................................... 180
Appendices 183
A Commonly used discrete distributions 185
B Commonly used continuous distributions 187
X
Contents
C Special distributions 189
C.l x2 distribution ........................................ 189
C.2 Student’s ¿-distribution............................... 189
C.3 ^-distribution.......................................... 190
D The Greek alphabet 191
E Mathematical notation 193
F Summation and product notation 195
G Exponentials and (natural) logarithms 199
H Subjective probability 201
References 205
Index
207
|
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| spelling | Thijssen, Jacco J. J. 1976- Verfasser (DE-588)171863267 aut A concise introduction to statistical inference Jacco Thijssen, the University of York, UK Boca Raton CRC Press, Taylor and Francis Group [2017] xix, 210 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier A> Chapman & Hall Book Includes bibliographical references and index Mathematical statistics Textbooks Probabilities Textbooks Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Inferenzstatistik (DE-588)4247120-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Statistik (DE-588)4056995-0 s Inferenzstatistik (DE-588)4247120-5 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Erscheint auch als Online-Ausgabe 9781498755801 Erscheint auch als Online-Ausgabe 9781498755795 Erscheint auch als Online-Ausgabe 9781498755788 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029606516&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Thijssen, Jacco J. J. 1976- A concise introduction to statistical inference Mathematical statistics Textbooks Probabilities Textbooks Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Inferenzstatistik (DE-588)4247120-5 gnd |
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| title | A concise introduction to statistical inference |
| title_auth | A concise introduction to statistical inference |
| title_exact_search | A concise introduction to statistical inference |
| title_full | A concise introduction to statistical inference Jacco Thijssen, the University of York, UK |
| title_fullStr | A concise introduction to statistical inference Jacco Thijssen, the University of York, UK |
| title_full_unstemmed | A concise introduction to statistical inference Jacco Thijssen, the University of York, UK |
| title_short | A concise introduction to statistical inference |
| title_sort | a concise introduction to statistical inference |
| topic | Mathematical statistics Textbooks Probabilities Textbooks Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Inferenzstatistik (DE-588)4247120-5 gnd |
| topic_facet | Mathematical statistics Textbooks Probabilities Textbooks Statistik Wahrscheinlichkeitsrechnung Inferenzstatistik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029606516&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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