A mathematical primer for social statistics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Los Angeles [u.a.]
Sage
2009
|
| Edition: | [Nachdr.] |
| Series: | Series: Quantitative applications in the social sciences
159 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 165) and index |
| Physical Description: | XIV, 170 S. graph. Darst. |
| ISBN: | 9781412960809 |
Staff View
MARC
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| 264 | 1 | |a Los Angeles [u.a.] |b Sage |c 2009 | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
About the Author viii
Series Editor s Introduction ix
Preface xi
Notation xii
Acknowledgments xiv
1. Matrices, Linear Algebra, and Vector Geometry 1
1.1 Matrices 2
1.1.1 Introducing the Actors: Basic Definitions 2
1.1.2 Simple Matrix Arithmetic 5
1.1.3 Matrix Inverses 11
1.1.4 Determinants 16
1.1.5 The Kronecker Product 16
1.2 Basic Vector Geometry 18
1.3 Vector Spaces and Subspaces 20
1.3.1 Orthogonality and Orthogonal Projections 24
1.4 Matrix Rank and the Solution of Linear
Simultaneous Equations 30
1.4.1 Rank 30
1.4.2 Linear Simultaneous Equations 32
1.4.3 Generalized Inverses 37
1.5 Eigenvalues and Eigenvectors 41
1.6 Quadratic Forms and Positive-Definite Matrices 45
1.6.1 The Cholesky Decomposition 46
1.7 Recommended Reading 47
2. An Introduction to Calculus 48
2.1 Review 48
.1 Numbers 48
.2 Lines and Planes 49
.3 Polynomials 51
.4 Logarithms and Exponentials 52
.5 Basic Trigonometric Functions 54
2.2 Limits 55
2.2.1 The Epsilon-Delta Definition of a Limit 56
2.2.2 Finding a Limit: An Example 57
2.2.3 Rules for Manipulating Limits 58
2.3 The Derivative of a Function 59
2.3.1 The Derivative as the Limit of
the Difference Quotient: An Example 61
2.3.2 Derivatives of Powers 61
2.3.3 Rules for Manipulating Derivatives 62
2.3.4 Derivatives of Logs and Exponentials 65
2.3.5 Derivatives of the Basic Trigonometric Functions 65
2.3.6 Second-Order and Higher-Order Derivatives 66
2.4 Optimization 66
2.4.1 Optimization: An Example 68
2.5 Multivariable and Matrix Differential Calculus 71
2.5.1 Partial Derivatives 71
2.5.2 Lagrange Multipliers for Constrained Optimization 73
2.5.3 Differential Calculus in Matrix Form 74
2.6 Taylor Series 77
2.7 Essential Ideas of Integral Calculus 79
2.7.1 Areas: Definite Integrals 79
2.7.2 Indefinite Integrals 80
2.7.3 The Fundamental Theorem of Calculus 81
2.8 Recommended Reading 83
3. Probability and Estimation 84
3.1 Elementary Probability Theory 84
3.1.1 Probability Basics 84
3.1.2 Random Variables 89
3.1.3 Transformations of Random Variables 96
3.2 Some Discrete Probability Distributions 98
3.2.1 The Binomial and Bernoulli Distributions 99
3.2.2 The Multinomial Distributions 100
3.2.3 The Poisson Distributions 101
3.2.4 The Negative Binomial Distributions 102
3.3 Some Continuous Distributions 103
3.3.1 The Normal Distributions 103
3.3.2 The Chi-Square (x:) Distributions 105
3.3.3 Student s /-Distributions 106
3.3.4 The F-Distributions 107
3.3.5 The Multivariate-Normal Distributions 109
3.3.6 The Exponential Distributions 109
3.3.7 The Inverse-Gaussian Distributions 110
3.3.8 The Gamma Distributions 111
3.3.9 The Beta Distributions 112
3.4 Asymptotic Distribution Theory: An Introduction 113
3.4.1 Probability Limits 113
3.4.2 Asymptotic Expectation and Variance 115
3.4.3 Asymptotic Distribution 117
3.4.4 Vector and Matrix Random Variables 118
3.5 Properties of Estimators 119
3.5.1 Bias 119
3.5.2 Mean-Squared Error and Efficiency 120
3.5.3 Consistency 121
3.5.4 Sufficiency 122
3.5.5 Robustness 123
3.6 Maximum-Likelihood Estimation 131
3.6.1 Preliminary Example 131
3.6.2 Properties of Maximum-Likelihood Estimators 134
3.6.3 Statistical Inference: Wald, Likelihood-Ratio,
and Score Tests 135
3.6.4 Several Parameters 139
3.6.5 The Delta Method 143
3.7 Introduction to Bayesian Inference 144
3.7.1 Bayes s Theorem 144
3.7.2 Extending Bayes s Theorem 146
3.7.3 An Example of Bayesian Inference 148
3.7.4 Bayesian Interval Estimates 150
3.7.5 Bayesian Inference for Several Parameters 151
3.8 Recommended Reading 151
4. Putting the Math to Work: Linear Least-Squares Regression 152
4.1 Least-Squares Fit 152
4.2 A Statistical Model for Linear Regression 155
4.3 The Least-Squares Coefficients as Estimators 156
4.4 Statistical Inference for the Regression Model 157
4.5 Maximum-Likelihood Estimation of the Regression Model 160
4.6 Random Xs 161
References 165
Index 166
|
| any_adam_object | 1 |
| author | Fox, John 1947- |
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| callnumber-first | H - Social Science |
| callnumber-label | H61 |
| callnumber-raw | H61.25 |
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| callnumber-subject | H - Social Science |
| classification_rvk | MR 2100 MR 2200 |
| ctrlnum | (OCoLC)213480000 (DE-599)BSZ279266316 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Soziologie Mathematik |
| edition | [Nachdr.] |
| format | Book |
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| genre_facet | Einführung |
| id | DE-604.BV024123048 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:57:57Z |
| institution | BVB |
| isbn | 9781412960809 |
| language | English |
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| physical | XIV, 170 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Sage |
| record_format | marc |
| series | Series: Quantitative applications in the social sciences |
| series2 | Series: Quantitative applications in the social sciences |
| spelling | Fox, John 1947- Verfasser (DE-588)132520346 aut A mathematical primer for social statistics John Fox [Nachdr.] Los Angeles [u.a.] Sage 2009 XIV, 170 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series: Quantitative applications in the social sciences 159 Includes bibliographical references (p. 165) and index Mathematik Sozialwissenschaften Social sciences Mathematics Social sciences Statistical methods Sozialwissenschaften (DE-588)4055916-6 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Sozialwissenschaften (DE-588)4055916-6 s Statistik (DE-588)4056995-0 s DE-604 Series: Quantitative applications in the social sciences 159 (DE-604)BV000005102 159 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018339770&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fox, John 1947- A mathematical primer for social statistics Series: Quantitative applications in the social sciences Mathematik Sozialwissenschaften Social sciences Mathematics Social sciences Statistical methods Sozialwissenschaften (DE-588)4055916-6 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4055916-6 (DE-588)4056995-0 (DE-588)4151278-9 |
| title | A mathematical primer for social statistics |
| title_auth | A mathematical primer for social statistics |
| title_exact_search | A mathematical primer for social statistics |
| title_full | A mathematical primer for social statistics John Fox |
| title_fullStr | A mathematical primer for social statistics John Fox |
| title_full_unstemmed | A mathematical primer for social statistics John Fox |
| title_short | A mathematical primer for social statistics |
| title_sort | a mathematical primer for social statistics |
| topic | Mathematik Sozialwissenschaften Social sciences Mathematics Social sciences Statistical methods Sozialwissenschaften (DE-588)4055916-6 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Mathematik Sozialwissenschaften Social sciences Mathematics Social sciences Statistical methods Statistik Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018339770&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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