Mathematical statistics for applied econometrics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2015
|
| Series: | A Chapman & Hall book
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XX, 343 S. graph. Darst. |
| ISBN: | 9781466594098 |
Staff View
MARC
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| 245 | 1 | 0 | |a Mathematical statistics for applied econometrics |c Charles B. Moss |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2015 | |
| 300 | |a XX, 343 S. |b graph. Darst. | ||
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| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Wirtschaft | |
| 650 | 4 | |a Econometrics | |
| 650 | 4 | |a Economics |x Mathematical models | |
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Record in the Search Index
| _version_ | 1804153191850311680 |
|---|---|
| adam_text | Contents
List of Figures
xiii
List of Tables
xv
Preface
xix
1
Defining Mathematical Statistics
1
1.1
Mathematical Statistics and Econometrics
.......... 3
1.1.1
Econometrics and Scientific Discovery
......... 5
1.1.2
Econometrics and Planning
............... 12
1.2
Mathematical Statistics and Modeling Economic Decisions
. 14
1.3
Chapter Summary
........................ 17
1.4
Review Questions
........................ 18
1 Defining Random Variables
19
2
Introduction to Statistics, Probability, and Econometrics
21
2.1
Two Definitions of Probability for Econometrics
....... 27
2.1.1
Counting Techniques
................... 28
2.1.2
Axiomatic Foundations
................. 32
2.2
What Is Statistics?
....................... 38
2.3
Chapter Summary
........................ 39
2.4
Review Questions
........................ 40
2.5
Numerical Exercises
....................... 40
3
Random Variables and Probability Distributions
43
3.1
Uniform Probability Measure
.................. 44
3.2
Random Variables and Distributions
.............. 50
3.2.1
Discrete Random Variables
............... 51
3.2.2
Continuous Random Variables
............. 52
3.3
Conditional Probability and Independence
.......... 55
3.3.1
Conditional Probability and Independence for Discrete
Random Variables
.................... 57
3.3.2
Conditional Probability and Independence for Continu¬
ous Random Variables
.................. 61
3.4
Cumulative Distribution Function
............... 71
vii
viii Contents
3.5
Some Useful Distributions
................... 71
3.6
Change of Variables
....................... 75
3.7
Derivation of the Normal Distribution Function
....... 76
3.8
An Applied Sabbatical
..................... 81
3.9
Chapter Summary
........................ 83
3.10
Review Questions
........................ 84
3.11
Numerical Exercises
....................... 85
4
Moments and Moment-Generating Functions
87
4.1
Expected Values
......................... 87
4.2
Moments
............................. 96
4.3
Covariance and Correlation
................... 97
4.4
Conditional Mean and Variance
................ 103
4.5
Moment-Generating Functions
................. 105
4.5.1
Moment-Generating Functions for Specific
Distributions
....................... 106
4.6
Chapter Summary
........................ 109
4.7
Review Questions
........................ 110
4.8
Numerical Exercises
....................... 110
5
Binomial and Normal Random Variables
113
5.1
Bernoulli and Binomial Random Variables
.......... 114
5.2
Univariate Normal Distribution
................ 117
5.3
Linking the Normal Distribution to the Binomial
....... 120
5.4
Divariate
and Multivariate Normal Random Variables
.... 122
5.4.1
Bivariate Normal Random Variables
.......... 124
5.4.2
Multivariate Normal Distribution
............ 127
5.5
Chapter Summary
........................ 129
5.6
Review Questions
........................ 129
5.7
Numerical Exercises
....................... 130
II Estimation
131
6
Large Sample Theory
133
6.1
Convergence of Statistics
.................... 133
6.2
Modes of Convergence
...................... 137
6.2.1
Almost Sure Convergence
................ 140
6.2.2
Convergence in Probability
............... 142
6.2.3
Convergence in tli€i rth Mean
.............. 142
6.3
Laws of Large Numbers
..................... 144
6.4
Asymptotic Normality
...................... 145
6.5
Wrapping Up Loose Ends
.................... 149
6.5.1
Application of Holder s Inequality
........... 149
6.5.2
Application of Chebychev s Inequality
......... 149
6.5.3
Normal Approximation of the Binomial
........ 150
Contents ix
6.6
Chapter Summary
........................ 150
6.7
Review Questions
........................ 151
6.8
Numerical Exercises
....................... 151
7
Point Estimation
153
7.1
Sampling and Sample Image
.................. 154
7.2
Familiar Estimators
....................... 160
7.2.1
Estimators in General
.................. 161
7.2.2
Nonparametric Estimation
................ 164
7.3
Properties of Estimators
.................... 165
7.3.1
Measures of Closeness
.................. 166
7.3.2
Mean Squared Error
................... 166
7.3.3
Strategies for Choosing an Estimator
.......... 169
7.3.4
Best Linear Unbiased Estimator
............ 169
7.3.5
Asymptotic Properties
.................. 172
7.3.6
Maximum Likelihood
................... 172
7.4
Sufficient Statistics
....................... 173
7.4.1
Data Reduction
...................... 173
7.4.2
Sufficiency Principle
................... 174
7.5
Concentrated Likelihood Functions
.............. 176
7.6
Normal Equations
........................ 177
7.7
Properties of Maximum Likelihood Estimators
........ 178
7.8
Chapter Summary
........................ 180
7.9
Review Questions
........................ 181
7.10
Numerical Exercises
....................... 181
8
Interval Estimation
183
8.1
Confidence Intervals
....................... 183
8.2
Bayesian Estimation
....................... 192
8.3
Bayesian Confidence Intervals
................. 195
8.4
Chapter Summary
........................ 195
8.5
Review Questions
........................ 196
8.6
Numerical Exercises
....................... 196
9
Testing Hypotheses
199
9.1
Type I and Type II Errors
................... 201
9.2
Neyman-Pearson Lemma
.................... 203
9.3
Simple Tests against a Composite
............... 205
9.4
Composite against a Composite
................ 207
9.5
Testing Hypotheses about Vectors
............... 210
9.6
Delta Method
.......................... 211
9.7
Chapter Summary
........................ 212
9.8
Review Questions
........................ 213
9.9
Numerical Exercises
....................... 213
x
Contents
III Econometric
Applications
215
10
Elements of Matrix Analysis
217
10.1
Review of Elementary Matrix Algebra
............. 218
10.1.1
Basic Definitions
..................... 218
10.1.2
Vector Spaces
....................... 227
10.2
Projection Matrices
....................... 230
10.3
Idempotent Matrices
...................... 232
10.4
Eigenvalues and Eigenvectors
.................. 232
10.5 Kronecker
Products
....................... 234
10.6
Chapter Summary
........................ 236
10.7
Review Questions
........................ 236
10.8
Numerical Exercises
....................... 236
11
Regression Applications in Econometrics
239
11.1
Simple Linear Regression
.................... 240
11.1.1
Least Squares: A Mathematical Solution
........ 241
11.1.2
Best Linear Unbiased Estimator: A Statistical Solution
244
11.1.3
Conditional Normal Model
............... 247
11.1.4
Variance of the Ordinary Least Squares Estimator
. . 248
11.2
Multivariate Regression
..................... 249
11.2.1
Variance of Estimator
.................. 250
11.2.2
Gauss Markov Theorem
................. 251
11.3
Linear Restrictions
....................... 252
11.3.1
Variance of the Restricted Estimator
.......... 255
11.3.2
Testing Linear Restrictions
............... 255
11.4
Exceptions to Ordinary Least Squares
............. 256
11.4.1
Heteroscedasticity
.................... 257
11.4.2
Two Stage Least Squares and Instrumental Variables
. 261
11.4.3
Generalized Method of Moments Estimator
...... 264
11.5
Chapter Summary
........................ 268
11.6
Review Questions
........................ 269
11.7
Numerical Exercises
....................... 270
12
Survey of Nonlinear Econometric Applications
271
12.1
Nonlinear Least Squares and Maximum Likelihood
...... 271
12.2
Bayesian Estimation
....................... 278
12.2.1
Basic Model
........................ 278
12.2.2
Conditioning and Updating
............... 279
12.2.3
Simple Estimation by Simulation
............ 285
12.3
Least Absolute Deviation and Related Estimators
...... 286
12.3.1
Least Absolute Deviation
................ 288
12.3.2
Quantile Regression
................... 289
12.4
Chapter Summary
........................ 291
12.5
Review Questions
........................ 292
Contents xi
12.6
Numerical Exercises
....................... 292
13
Conclusions
295
Appendix A Symbolic Computer Programs
299
A.I Maxima
.............................. 299
A.2
Mathematica™
......................... 302
Appendix
В
Change of Variables for Simultaneous
Equations
307
B.I Linear Change in Variables
................... 308
B.2 Estimating a System of Equations
............... 311
Appendix
С
Fourier Transformations
319
C.I Continuing the Example
.................... 319
C.2 Fourier Approximation
..................... 323
Appendix
D
Farm Interest Rate Data
325
Appendix
E
Nonlinear Optimization
327
E.I Hessian Matrix of Three-Parameter Cobb-Douglas
...... 327
E.2 Bayesian Estimation
....................... 329
E.3 Least Absolute Deviation Estimator
.............. 330
Glossary
333
References
337
Index
341
|
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| id | DE-604.BV042470157 |
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| institution | BVB |
| isbn | 9781466594098 |
| language | English |
| lccn | 014028241 |
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| physical | XX, 343 S. graph. Darst. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | CRC Press |
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| series2 | A Chapman & Hall book |
| spelling | Moss, Charles B. Verfasser (DE-588)128729856 aut Mathematical statistics for applied econometrics Charles B. Moss Boca Raton [u.a.] CRC Press 2015 XX, 343 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Chapman & Hall book Includes bibliographical references and index Mathematisches Modell Wirtschaft Econometrics Economics Mathematical models Statistik (DE-588)4056995-0 gnd rswk-swf Ökonometrie (DE-588)4132280-0 gnd rswk-swf Ökonometrie (DE-588)4132280-0 s Statistik (DE-588)4056995-0 s b DE-604 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=027905341&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moss, Charles B. Mathematical statistics for applied econometrics Mathematisches Modell Wirtschaft Econometrics Economics Mathematical models Statistik (DE-588)4056995-0 gnd Ökonometrie (DE-588)4132280-0 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4132280-0 |
| title | Mathematical statistics for applied econometrics |
| title_auth | Mathematical statistics for applied econometrics |
| title_exact_search | Mathematical statistics for applied econometrics |
| title_full | Mathematical statistics for applied econometrics Charles B. Moss |
| title_fullStr | Mathematical statistics for applied econometrics Charles B. Moss |
| title_full_unstemmed | Mathematical statistics for applied econometrics Charles B. Moss |
| title_short | Mathematical statistics for applied econometrics |
| title_sort | mathematical statistics for applied econometrics |
| topic | Mathematisches Modell Wirtschaft Econometrics Economics Mathematical models Statistik (DE-588)4056995-0 gnd Ökonometrie (DE-588)4132280-0 gnd |
| topic_facet | Mathematisches Modell Wirtschaft Econometrics Economics Mathematical models Statistik Ökonometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027905341&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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