Mathematical statistics for economics and business:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
1999
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| Ausgabe: | Corr. 3. print. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XVIII, 723 S. graph. Darst. |
| ISBN: | 0387945873 |
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| 100 | 1 | |a Mittelhammer, Ron C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical statistics for economics and business |c Ron C. Mittelhammer |
| 250 | |a Corr. 3. print. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 1999 | |
| 300 | |a XVIII, 723 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Wirtschaftsstatistik |0 (DE-588)4066517-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804137288417935360 |
|---|---|
| adam_text | Contents
Preface
vii
1. Elements
of
Probability
Theory
1
1.1.
Introduction
1
1.2.
Experiment, Sample Space, Outcome, and Event
2
1.3.
Nonaxiomatic Probability Definitions
5
1.4.
Axiomatic Definition of Probability
8
1.5.
Some Probability Theorems
15
1.6.
A Digression on Events
20
1.7.
Conditional Probability
22
1.8.
Independence
29
1.9.
Bayes s Rule
34
Key Words, Phrases, and Symbols
36
Problems
37
2.
Random Variables, Densities, and Cumulative Distribution
Functions
43
2.1.
Introduction
43
2.2.
Univariate Random Variables and Density Functions
44
xii Contents
Probability
Space
Induced by a Random Variable
45
Discrete Random Variables and Probability Density
Functions
48
Continuous Random Variables and Probability Density
Functions
51
Classes of Discrete and Continuous PDFs
55
Mixed Discrete-Continuous Random Variables
58
2.3.
Univariate Cumulative Distribution Functions
60
CDF Properties
63
Duality Between CDFs and PDFs
65
2.4.
Multivariate Random Variables, PDFs, and CDFs
67
Multivariate Random Variable Properties and Classes of
PDFs
69
Multivariate CDFs and Duality with PDFs
72
Multivariate Mixed Discrete-Continuous and Composite
Random Variables
76
2.5.
Marginal Probability Density Functions and CDFs
77
Bivariate Case
77
N-
Variate
Case
81
Marginal Cumulative Distribution Functions (MCDFsj
83
2.6.
Conditional Density Functions
83
Bivariate Case
84
Conditioning on Elementary Events in Continuous Cases
86
N-Variate Case
88
Conditional CDFs
89
2.7.
Independence of Random Variables
90
Bivariate Case
90
N-Variate
93
Independence Between Random Vectors and Between
Functions of Random Vectors
95
2.8.
Extended Example of Multivariate Concepts in the
Continuous Case
97
2.9.
Events Occurring with Probability Zero
100
Key Words, Phrases, and Symbols
101
Problems
101
3.
Mathematical Expectation and Moments
109
3.1.
Expectation of a Random Variable
109
3.2.
Expectation of a Function of Random Variables
116
Expectation Properties
121
Multivariate Extensions
122
3.3.
Conditional Expectation
125
Regression Function
129
Conditional Expectation and Regression in the Multivariate
Case
130
Contents _____________________________________________________xiii
3.4. Moments
of a Random
Variable 132
Relationship Between Moments About the Origin and Mean
137
Existence of Moments
138
Nonmoment
Measures of Probability Density Characteristics
139
3.5.
Moment- and Cumulant-Generating Functions
141
Uniqueness and Inversion of MGFs
143
Cumulant-Generating Function
145
Multivariate Extensions
146
3.6.
Joint Moments, Covariance, and Correlation
148
Covariance and Correlation
148
Correlation, Linear Association, and Degeneracy
152
3.7.
Means and Variances of Linear Combinations of Random
Variables
156
3.8.
Necessary and Sufficient Conditions for Positive
Semidefmiteness
161
Key Words, Phrases, and Symbols
162
Problems
162
4.
Parametric Families of Density Functions
169
4.1.
Parametric Families of Discrete Density Functions
170
Family Name: Uniform
170
Family Name: Bernoulli
171
Family Name: Binomial
172
Family Name: Multinomial
174
Family Name: Negative Binomial and Geometric
175
Family Name:
Poisson
177
Family Name: Hypergeometric
183
Family Name: Multivariate Hypergeometric
185
4.2.
Parametric Families of Continuous Density Functions
186
Family Name: Uniform
186
Family Name: Gamma
187
Gamma Subfamily Name: Exponential
190
Gamma Subfamily Name: Chi-Square
192
Family Name: Beta
194
4.3.
The Normal Family of Densities
197
Family Name: Univariate Normal
197
Family Name: Multivariate Normal Density
202
4.4.
The Exponential Class of Densities
213
Key Words, Phrases, and Symbols
215
Problems
216
5.
Basic
Asy
mptotics
221
5.1.
Introduction
221
5.2.
Elements of Real Analysis
222
xiv Contents
Limit
of a Sequence
224
Continuous Functions
228
Convergence of Function Sequence
230
Order of Magnitude of a Sequence
231
5.3.
Types of Random-Variable Convergence
233
Convergence in Distribution
234
Convergence in Probability
241
Convergence in Mean Square (or Convergence in Quadratic
Mean)
249
Almost-Sure Convergence (or Convergence with
Probability
1) 253
Relationships Between Convergence Modes
258
5.4.
Laws of Large Numbers
258
Weak Laws of Large Numbers (WLLN)
259
Strong Laws of Large Numbers (SLLN)
263
5.5.
Central Limit Theorems
268
Independent Scalar Random Variables
269
Dependent Random Variables
281
Multivariate Central Limit Results
282
5.6.
Asymptotic Distributions of Differentiable Functions of
Asymptotically Normally Distributed Random Variables
286
Key Words, Phrases, and Symbols
290
Problems
291
6.
Sampling, Sample Moments, Sampling Distributions, and
Simulation
297
6.1.
Introduction
297
6.2.
Random Sampling
299
Random Sampling from a Population Distribution
300
Random Sampling Without Replacement
303
Sample Generated by a Composite Experiment
305
Commonalities in Probabilistic Structure of Random
Samples
306
Statistics
307
6.3.
Empirical or Sample Distribution Function
308
EDF: Scalar Case
308
EDF: Multivariate Case
313
6.4.
Sample Moments and Sample Correlation
314
Scalar Case
314
Multivariate Case
320
6.5.
Properties of Xn and
S„
When Random Sampling from a
Normal Distribution
328
6.6.
Sampling Distributions: Deriving Probability Densities of
Functions of Random Variables
331
MGF Approach
332
Contents___________________________________________________________xv
CDF Approach
332
Equivalent Events Approach (Discrete Case)
334
Change of Variables (Continuous Case)
335
6.7.
t-and F-Densities
341
i-Density
341
Family Name: t-Family
343
F-Density
345
Family Name: F-Family
346
6.8.
Random Sample Simulation and the Probability Integral
Transformation
348
6.9.
Order Statistics
351
Key Words, Phrases, and Symbols
355
Problems
356
7.
Elements of Point Estimation Theory
363
7.1.
Introduction
363
7.2.
Statistical Models
365
7.3.
Estimators and Estimator Properties
370
Estimators
370
Estimator Properties
371
Finite Sample Properties
373
Asymptotic Properties
383
Class of Consistent Asymptotically Normal (CAN)
Estimators and Asymptotic Properties
385
7.4.
Sufficient Statistics
389
Minimal Sufficient Statistics
393
Sufficient Statistics in the Exponential Class
397
Sufficiency and the
MSE
Criterion
398
Complete Sufficient Statistics
400
Sufficiency, Minimality, and Completeness of Functions of
Sufficient Statistics
404
7.5.
Results on MVUE Estimation
405
Cramér-Rao
Lower Bound
408
Complete Sufficient Statistics and MVUEs
420
Key Words, Phrases, and Symbols
421
Problems
422
8.
Point Estimation Methods
427
8.1.
Introduction
427
8.2.
Least Squares and the General Linear Model
428
The Classical GLM Assumptions
429
Estimator for
β
Under Classical GLM Assumptions
433
Estimator for
аг Јпает
Classical GLM Assumptions
437
Consistency of
β
439
xvi Contents
Consistency of
S2
л
441
Asymptotic Normality of
β
443
Asymptotic Normality of
Ś2
447
Summary of Estimator Properties
449
Violations of Classic GLM Assumptions
452
GLM Assumption Violations: Property Summary and
Epilogue
459
Least Squares Under Normality
460
MVUE Property of
β
and S2
462
8.3.
The Method of Maximum Likelihood
464
MLE Mechanics
465
MLE Properties: Finite Sample
470
MLE Properties: Large Sample
472
MLE
Invariance
Principle
485
MLE Property Summary
489
8.4.
The Method of Moments
490
Method of Moments Estimator
491
MOM Estimator Properties
493
Generalized Method of Moments (GMM)
Estimator
495
GMM Properties
497
Key Words, Phrases, and Symbols
502
Problems
502
9.
Elements of Hypothesis-Testing Theory
509
9.1.
Introduction
509
9.2.
Statistical Hypotheses
510
9.3.
Basic Hypothesis-Testing Concepts
514
Statistical Hypothesis Tests
514
Type I Error, Type II Error, and Ideal Statistical
Tests
516
Controlling Type I and II Errors
519
Type I/Type
Π
Error Tradeoff
522
Test Statistics
526
Null and Alternative Hypotheses
527
9.4.
Parametric Hypothesis Tests and Test Properties
527
Maintained Hypothesis
529
Power Function
530
Properties of Statistical Tests
531
Ρ
Values
535
Asymptotic Tests
538
9.5.
Results on UMP Tests
539
Neyman-Pearson Approach
539
Monotone Likelihood Ratio Approach
550
Exponential Class of Densities
556
Contents________________________________________________________xvii
*Conditioning in
the
Multiple Parameter
Case
571
Concluding Remarks
586
9.6.
Noncentral
í-Distribution
586
Family Name: Noncentral t-Distribution
586
Key Words, Phrases, and Symbols
588
Problems
589
10.
Hypothesis-Testing Methods
595
10.1.
Introduction
595
10.2.
Heuristic Approach
596
10.3.
Generalized Likelihood Ratio Tests
601
Test Properties: Finite Sample
602
Test Properties: Asymptotics
608
10.4. Lagrange
Multiplier Tests
616
10.5. Wald
Tests
622
10.6.
Tests in the GLM
625
Tests When
є
Is Multivariate Normal
625
Testing R/3
=
r,
Rß <
t,
Or R/3
>
r
When
R
Is
(1
x
A):
T-Tests
628
Bonferroni Joint Tests of Rj/3
=
r,,
Ri/3
<
ђ,
or R,/3
>
i,·,
1 = 1,...,
m
631
Testing When
є
Is Not Multivariate Normal
635
Testing
Rß =
r
or R(/3)
=
r
When
R
Has
q
Rows:
Asymptotic x2-Tests
636
Testing
R[ß) =
r,
R[ß) <
ι,
or
Riß) >
τ
When
JÎ
Is a
Scalar Function: Asymptotic Normal Tests
636
10.7.
Confidence Intervals and Regions
640
Defining Confidence Regions via Duality with Critical
Regions
642
Properties of Confidence Regions
647
Confidence Regions from Pivotal Quantities
649
Confidence Regions as Hypothesis Tests
654
10.8.
Nonparametrie Tests of Distributional Assumptions
654
Functional Forms of Probability Distributions
655
HD
Assumption
663
10.9.
Noncentral
χ2-
and F-Distributions
666
Family Name:
Noncentral
χ2
-Distribution
666
Family Name:
Noncentral F-Distribution
667
Key Words, Phrases, and Symbols
668
Problems
669
Appendix A. Math Review: Sets, Functions, Permutations,
Combinations, and Notation
677
А.1.
Introduction
677
xviii Contents
A.2.
Definitions,
Axioms, Theorems,
Corollaries, and
Lemmas 677
A.3. Elements
of Set Theory
679
Set-Defining Methods
680
Set Classifications
681
Special Sets, Set Operations, and Set Relationships
682
Rules Governing Set Operations
684
A.4. Relations, Point Functions, and Set Functions
687
Cartesian Product
688
Relation (Binary)
689
Function
691
Real-Valued Point Versus Set Functions
693
A.5. Combinations and Permutations
696
A.6. Summation, Integration and Matrix Differentiation Notation
699
Key Words, Phrases, and Symbols
701
Problems
702
Appendix B. Useful Tables
705
B.I. Cumulative Normal Distribution
706
B.2. Student s
t
Distribution
707
B.3. Chi-square Distribution
708
B.4. F-Distribution:
5%
Points
710
B.5.
ľ-Distribution:
1%
Points
712
Index
715
This textbook provides a comprehensive introduction to the principles of mathematical
statistics which underpin statistical analyses
m
the fields of economics, business, and
econometrics. The selection of topics is designed to provide students with a substantial
understanding of statistical applications in these subjects.
After introducing the concepts of probability, random variables» and probability den-
sit}· functions» the author develops the key concepts of mathematical statistics, notably:
expectation, sampling, asymptotics, and the main families of distributions. The latter
half of the book is then devoted to the theories of estimation and hypothesis testing with
associated examples and problems that indicate their wide applicability in economics
and business.
The book has evolved
from
numerous graduate courses in mathematical statistics and
econometrics taught by the author and so will be ideal for students beginning graduate
study as well as for advanced seniors. Hundreds of exercises and problems are provided.
|
| adam_txt |
Contents
Preface
vii
1. Elements
of
Probability
Theory
1
1.1.
Introduction
1
1.2.
Experiment, Sample Space, Outcome, and Event
2
1.3.
Nonaxiomatic Probability Definitions
5
1.4.
Axiomatic Definition of Probability
8
1.5.
Some Probability Theorems
15
1.6.
A Digression on Events
20
1.7.
Conditional Probability
22
1.8.
Independence
29
1.9.
Bayes's Rule
34
Key Words, Phrases, and Symbols
36
Problems
37
2.
Random Variables, Densities, and Cumulative Distribution
Functions
43
2.1.
Introduction
43
2.2.
Univariate Random Variables and Density Functions
44
xii Contents
Probability
Space
Induced by a Random Variable
45
Discrete Random Variables and Probability Density
Functions
48
Continuous Random Variables and Probability Density
Functions
51
Classes of Discrete and Continuous PDFs
55
Mixed Discrete-Continuous Random Variables
58
2.3.
Univariate Cumulative Distribution Functions
60
CDF Properties
63
Duality Between CDFs and PDFs
65
2.4.
Multivariate Random Variables, PDFs, and CDFs
67
Multivariate Random Variable Properties and Classes of
PDFs
69
Multivariate CDFs and Duality with PDFs
72
Multivariate Mixed Discrete-Continuous and Composite
Random Variables
76
2.5.
Marginal Probability Density Functions and CDFs
77
Bivariate Case
77
N-
Variate
Case
81
Marginal Cumulative Distribution Functions (MCDFsj
83
2.6.
Conditional Density Functions
83
Bivariate Case
84
Conditioning on Elementary Events in Continuous Cases
86
N-Variate Case
88
Conditional CDFs
89
2.7.
Independence of Random Variables
90
Bivariate Case
90
N-Variate
93
Independence Between Random Vectors and Between
Functions of Random Vectors
95
2.8.
Extended Example of Multivariate Concepts in the
Continuous Case
97
2.9.
Events Occurring with Probability Zero
100
Key Words, Phrases, and Symbols
101
Problems
101
3.
Mathematical Expectation and Moments
109
3.1.
Expectation of a Random Variable
109
3.2.
Expectation of a Function of Random Variables
116
Expectation Properties
121
Multivariate Extensions
122
3.3.
Conditional Expectation
125
Regression Function
129
Conditional Expectation and Regression in the Multivariate
Case
130
Contents _xiii
3.4. Moments
of a Random
Variable 132
Relationship Between Moments About the Origin and Mean
137
Existence of Moments
138
Nonmoment
Measures of Probability Density Characteristics
139
3.5.
Moment- and Cumulant-Generating Functions
141
Uniqueness and Inversion of MGFs
143
Cumulant-Generating Function
145
Multivariate Extensions
146
3.6.
Joint Moments, Covariance, and Correlation
148
Covariance and Correlation
148
Correlation, Linear Association, and Degeneracy
152
3.7.
Means and Variances of Linear Combinations of Random
Variables
156
3.8.
Necessary and Sufficient Conditions for Positive
Semidefmiteness
161
Key Words, Phrases, and Symbols
162
Problems
162
4.
Parametric Families of Density Functions
169
4.1.
Parametric Families of Discrete Density Functions
170
Family Name: Uniform
170
Family Name: Bernoulli
171
Family Name: Binomial
172
Family Name: Multinomial
174
Family Name: Negative Binomial and Geometric
175
Family Name:
Poisson
177
Family Name: Hypergeometric
183
Family Name: Multivariate Hypergeometric
185
4.2.
Parametric Families of Continuous Density Functions
186
Family Name: Uniform
186
Family Name: Gamma
187
Gamma Subfamily Name: Exponential
190
Gamma Subfamily Name: Chi-Square
192
Family Name: Beta
194
4.3.
The Normal Family of Densities
197
Family Name: Univariate Normal
197
Family Name: Multivariate Normal Density
202
4.4.
The Exponential Class of Densities
213
Key Words, Phrases, and Symbols
215
Problems
216
5.
Basic
Asy
mptotics
221
5.1.
Introduction
221
5.2.
Elements of Real Analysis
222
xiv Contents
Limit
of a Sequence
224
Continuous Functions
228
Convergence of Function Sequence
230
Order of Magnitude of a Sequence
231
5.3.
Types of Random-Variable Convergence
233
Convergence in Distribution
234
Convergence in Probability
241
Convergence in Mean Square (or Convergence in Quadratic
Mean)
249
'Almost-Sure Convergence (or Convergence with
Probability
1) 253
Relationships Between Convergence Modes
258
5.4.
Laws of Large Numbers
258
Weak Laws of Large Numbers (WLLN)
259
'Strong Laws of Large Numbers (SLLN)
263
5.5.
Central Limit Theorems
268
Independent Scalar Random Variables
269
'Dependent Random Variables
281
Multivariate Central Limit Results
282
5.6.
Asymptotic Distributions of Differentiable Functions of
Asymptotically Normally Distributed Random Variables
286
Key Words, Phrases, and Symbols
290
Problems
291
6.
Sampling, Sample Moments, Sampling Distributions, and
Simulation
297
6.1.
Introduction
297
6.2.
Random Sampling
299
Random Sampling from a Population Distribution
300
Random Sampling Without Replacement
303
Sample Generated by a Composite Experiment
305
Commonalities in Probabilistic Structure of Random
Samples
306
Statistics
307
6.3.
Empirical or Sample Distribution Function
308
EDF: Scalar Case
308
EDF: Multivariate Case
313
6.4.
Sample Moments and Sample Correlation
314
Scalar Case
314
Multivariate Case
320
6.5.
Properties of Xn and
S„
When Random Sampling from a
Normal Distribution
328
6.6.
Sampling Distributions: Deriving Probability Densities of
Functions of Random Variables
331
MGF Approach
332
Contents_xv
CDF Approach
332
Equivalent Events Approach (Discrete Case)
334
Change of Variables (Continuous Case)
335
6.7.
t-and F-Densities
341
i-Density
341
Family Name: t-Family
343
F-Density
345
Family Name: F-Family
346
6.8.
Random Sample Simulation and the Probability Integral
Transformation
348
6.9.
Order Statistics
351
Key Words, Phrases, and Symbols
355
Problems
356
7.
Elements of Point Estimation Theory
363
7.1.
Introduction
363
7.2.
Statistical Models
365
7.3.
Estimators and Estimator Properties
370
Estimators
370
Estimator Properties
371
Finite Sample Properties
373
Asymptotic Properties
383
Class of Consistent Asymptotically Normal (CAN)
Estimators and Asymptotic Properties
385
7.4.
Sufficient Statistics
389
Minimal Sufficient Statistics
393
Sufficient Statistics in the Exponential Class
397
Sufficiency and the
MSE
Criterion
398
Complete Sufficient Statistics
400
Sufficiency, Minimality, and Completeness of Functions of
Sufficient Statistics
404
7.5.
Results on MVUE Estimation
405
Cramér-Rao
Lower Bound
408
Complete Sufficient Statistics and MVUEs
420
Key Words, Phrases, and Symbols
421
Problems
422
8.
Point Estimation Methods
427
8.1.
Introduction
427
8.2.
Least Squares and the General Linear Model
428
The Classical GLM Assumptions
429
Estimator for
β
Under Classical GLM Assumptions
433
Estimator for
аг\Јпает
Classical GLM Assumptions
437
Consistency of
β
439
xvi Contents
Consistency of
S2
л
441
Asymptotic Normality of
β
443
Asymptotic Normality of
Ś2
447
Summary of Estimator Properties
449
Violations of Classic GLM Assumptions
452
GLM Assumption Violations: Property Summary and
Epilogue
459
Least Squares Under Normality
460
MVUE Property of
β
and S2
462
8.3.
The Method of Maximum Likelihood
464
MLE Mechanics
465
MLE Properties: Finite Sample
470
MLE Properties: Large Sample
472
MLE
Invariance
Principle
485
MLE Property Summary
489
8.4.
The Method of Moments
490
Method of Moments Estimator
491
MOM Estimator Properties
493
Generalized Method of Moments (GMM)
Estimator
495
GMM Properties
497
Key Words, Phrases, and Symbols
502
Problems
502
9.
Elements of Hypothesis-Testing Theory
509
9.1.
Introduction
509
9.2.
Statistical Hypotheses
510
9.3.
Basic Hypothesis-Testing Concepts
514
Statistical Hypothesis Tests
514
Type I Error, Type II Error, and Ideal Statistical
Tests
516
Controlling Type I and II Errors
519
Type I/Type
Π
Error Tradeoff
522
Test Statistics
526
Null and Alternative Hypotheses
527
9.4.
Parametric Hypothesis Tests and Test Properties
527
Maintained Hypothesis
529
Power Function
530
Properties of Statistical Tests
531
Ρ
Values
535
Asymptotic Tests
538
9.5.
Results on UMP Tests
539
Neyman-Pearson Approach
539
Monotone Likelihood Ratio Approach
550
Exponential Class of Densities
556
Contents_xvii
*Conditioning in
the
Multiple Parameter
Case
571
Concluding Remarks
586
9.6.
Noncentral
í-Distribution
586
Family Name: Noncentral t-Distribution
586
Key Words, Phrases, and Symbols
588
Problems
589
10.
Hypothesis-Testing Methods
595
10.1.
Introduction
595
10.2.
Heuristic Approach
596
10.3.
Generalized Likelihood Ratio Tests
601
Test Properties: Finite Sample
602
Test Properties: Asymptotics
608
10.4. Lagrange
Multiplier Tests
616
10.5. Wald
Tests
622
10.6.
Tests in the GLM
625
Tests When
є
Is Multivariate Normal
625
Testing R/3
=
r,
Rß <
t,
Or R/3
>
r
When
R
Is
(1
x
A):
T-Tests
628
Bonferroni Joint Tests of Rj/3
=
r,,
Ri/3
<
ђ,
or R,/3
>
i,·,
1 = 1,.,
m
631
Testing When
є
Is Not Multivariate Normal
635
Testing
Rß =
r
or R(/3)
=
r
When
R
Has
q
Rows:
Asymptotic x2-Tests
636
Testing
R[ß) =
r,
R[ß) <
ι,
or
Riß) >
τ
When
JÎ
Is a
Scalar Function: Asymptotic Normal Tests
636
10.7.
Confidence Intervals and Regions
640
Defining Confidence Regions via Duality with Critical
Regions
642
Properties of Confidence Regions
647
Confidence Regions from Pivotal Quantities
649
Confidence Regions as Hypothesis Tests
654
10.8.
Nonparametrie Tests of Distributional Assumptions
654
Functional Forms of Probability Distributions
655
HD
Assumption
663
10.9.
Noncentral
χ2-
and F-Distributions
666
Family Name:
Noncentral
χ2
-Distribution
666
Family Name:
Noncentral F-Distribution
667
Key Words, Phrases, and Symbols
668
Problems
669
Appendix A. Math Review: Sets, Functions, Permutations,
Combinations, and Notation
677
А.1.
Introduction
677
xviii Contents
A.2.
Definitions,
Axioms, Theorems,
Corollaries, and
Lemmas 677
A.3. Elements
of Set Theory
679
Set-Defining Methods
680
Set Classifications
681
Special Sets, Set Operations, and Set Relationships
682
Rules Governing Set Operations
684
A.4. Relations, Point Functions, and Set Functions
687
Cartesian Product
688
Relation (Binary)
689
Function
691
Real-Valued Point Versus Set Functions
693
A.5. Combinations and Permutations
696
A.6. Summation, Integration and Matrix Differentiation Notation
699
Key Words, Phrases, and Symbols
701
Problems
702
Appendix B. Useful Tables
705
B.I. Cumulative Normal Distribution
706
B.2. Student's
t
Distribution
707
B.3. Chi-square Distribution
708
B.4. F-Distribution:
5%
Points
710
B.5.
ľ-Distribution:
1%
Points
712
Index
715
This textbook provides a comprehensive introduction to the principles of mathematical
statistics which underpin statistical analyses
m
the fields of economics, business, and
econometrics. The selection of topics is designed to provide students with a substantial
understanding of statistical applications in these subjects.
After introducing the concepts of probability, random variables» and probability den-
sit}· functions» the author develops the key concepts of mathematical statistics, notably:
expectation, sampling, asymptotics, and the main families of distributions. The latter
half of the book is then devoted to the theories of estimation and hypothesis testing with
associated examples and problems that indicate their wide applicability in economics
and business.
The book has evolved
from
numerous graduate courses in mathematical statistics and
econometrics taught by the author and so will be ideal for students beginning graduate
study as well as for advanced seniors. Hundreds of exercises and problems are provided. |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Mittelhammer, Ron C. |
| author_facet | Mittelhammer, Ron C. |
| author_role | aut |
| author_sort | Mittelhammer, Ron C. |
| author_variant | r c m rc rcm |
| building | Verbundindex |
| bvnumber | BV023054180 |
| callnumber-first | H - Social Science |
| callnumber-label | HF1017 |
| callnumber-raw | HF1017 |
| callnumber-search | HF1017 |
| callnumber-sort | HF 41017 |
| callnumber-subject | HF - Commerce |
| classification_rvk | QH 231 QH 240 SK 980 |
| ctrlnum | (OCoLC)247261467 (DE-599)BVBBV023054180 |
| 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 | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | Corr. 3. print. |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV023054180 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:25:56Z |
| indexdate | 2024-07-09T21:09:55Z |
| institution | BVB |
| isbn | 0387945873 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016257498 |
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| physical | XVIII, 723 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| spelling | Mittelhammer, Ron C. Verfasser aut Mathematical statistics for economics and business Ron C. Mittelhammer Corr. 3. print. New York, NY [u.a.] Springer 1999 XVIII, 723 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wirtschaftsstatistik (DE-588)4066517-3 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Wirtschaftsstatistik (DE-588)4066517-3 s DE-604 Statistik (DE-588)4056995-0 s 1\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016257498&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016257498&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mittelhammer, Ron C. Mathematical statistics for economics and business Wirtschaftsstatistik (DE-588)4066517-3 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4066517-3 (DE-588)4056995-0 (DE-588)4123623-3 |
| title | Mathematical statistics for economics and business |
| title_auth | Mathematical statistics for economics and business |
| title_exact_search | Mathematical statistics for economics and business |
| title_exact_search_txtP | Mathematical statistics for economics and business |
| title_full | Mathematical statistics for economics and business Ron C. Mittelhammer |
| title_fullStr | Mathematical statistics for economics and business Ron C. Mittelhammer |
| title_full_unstemmed | Mathematical statistics for economics and business Ron C. Mittelhammer |
| title_short | Mathematical statistics for economics and business |
| title_sort | mathematical statistics for economics and business |
| topic | Wirtschaftsstatistik (DE-588)4066517-3 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Wirtschaftsstatistik Statistik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016257498&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016257498&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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