Understanding advanced statistical methods:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton
CRC Press, Taylor & Francis Group
2013
|
| Schriftenreihe: | Texts in statistical science
A Chapman & Hall book |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xxv, 543 Seiten Diagramme |
| ISBN: | 9781466512108 |
Internformat
MARC
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| 100 | 1 | |a Westfall, Peter H. |d 1957- |e Verfasser |0 (DE-588)171276752 |4 aut | |
| 245 | 1 | 0 | |a Understanding advanced statistical methods |c Peter H. Westfal (Information Systems and Quantitative Sciences, Texas Tech University, USA), Kevin S. S. Henning (Department of Economics and International Business, Sam Houston State University, USA) |
| 264 | 1 | |a Boca Raton |b CRC Press, Taylor & Francis Group |c 2013 | |
| 300 | |a xxv, 543 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Texts in statistical science | |
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Datensatz im Suchindex
| _version_ | 1804152159211618304 |
|---|---|
| adam_text | Contents
List of Examples
..........................................................................................................................xiii
Preface
...........................................................................................................................................xix
Acknowledgments
....................................................................................................................xxiii
Authors
........................................................................................................................................xxv
1.
Introduction: Probability, Statistics, and Science
............................................................1
1.1
Reality, Nature, Science, and Models
.........................................................................1
1.2
Statistical Processes: Nature, Design and Measurement, and Data
......................3
1.3
Models
............................................................................................................................7
1.4
Deterministic Models
...................................................................................................8
1.5
Variability
.......................................................................................................................9
1.6
Parameters
....................................................................................................................11
1.7
Purely Probabilistic Statistical Models
....................................................................12
1.8
Statistical Models with Both Deterministic and Probabilistic Components
......16
1.9
Statistical Inference
.....................................................................................................18
1.10
Good and Bad Models
................................................................................................20
1.11
Uses of Probability Models
........................................................................................24
Vocabulary and Formula Summaries
..................................................................................30
Exercises
..................................................................................................................................32
2.
Random Variables and Their Probability Distributions
.............................................37
2.1
Introduction
.................................................................................................................37
2.2
Types of Random Variables: Nominal, Ordinal, and Continuous
.......................37
2.3
Discrete Probability Distribution Functions
...........................................................40
2.4
Continuous Probability Distribution Functions
.....................................................44
2.5
Some Calculus
—
Derivatives and Least Squares
....................................................58
2.6
More Calculus
—
Integrals and Cumulative Distribution Functions
...................65
Vocabulary and Formula Summaries
..................................................................................74
Exercises
..................................................................................................................................77
3.
Probability Calculation and Simulation
..........................................................................83
3.1
Introduction
.................................................................................................................83
3.2
Analytic Calculations, Discrete and Continuous Cases
........................................84
3.3
Simulation-Based Approximation
............................................................................86
3.4
Generating Random Numbers
..................................................................................87
Vocabulary and Formula Summaries
..................................................................................90
Exercises
..................................................................................................................................91
4.
Identifying Distributions
...................................................................................................95
4.1
Introduction
.................................................................................................................95
4.2
Identifying Distributions from Theory Alone
........................................................96
4.3
Using Data: Estimating Distributions via the Histogram
.....................................99
4.4
Quantiles: Theoretical and Data-Based Estimates
...............................................105
4.5
Using Data: Comparing Distributions via the Quantile-Quantile Plot
...........108
4.6
Effect of Randomness on Histograms and q-q Plots
...........................................110
vii
Contents
Vocabulary and Formula Summaries
................................................................................
ИЗ
Exercises
................................................................................................................................
П4
5.
Conditional Distributions and Independence
.............................................................
H7
5.1
Introduction
...............................................................................................................
П7
5.2
Conditional Discrete Distributions
........................................................................
И9
5.3
Estimating Conditional Discrete Distributions
....................................................121
5.4
Conditional Continuous Distributions
..................................................................122
5.5
Estimating Conditional Continuous Distributions
..............................................124
5.6
Independence
.............................................................................................................125
Vocabulary and Formula Summaries
................................................................................132
Exercises
................................................................................................................................133
6.
Marginal Distributions, Joint Distributions, Independence, and
Bayes
Theorem
................................................................................................................................137
6.1
Introduction
...............................................................................................................137
6.2
Joint and Marginal Distributions
...........................................................................139
6.3
Estimating and Visualizing Joint Distributions
...................................................145
6.4
Conditional Distributions from Joint Distributions
............................................147
6.5
Joint Distributions When Variables Are Independent
.........................................150
6.6
Bayes
Theorem
.........................................................................................................153
Vocabulary and Formula Summaries
................................................................................160
Exercises
................................................................................................................................161
7.
Sampling from Populations and Processes
...................................................................165
7.1
Introduction
...............................................................................................................165
7.2
Sampling from Populations
.....................................................................................167
7.3
Critique of the Population Interpretation of Probability Models
.......................172
7.3.1
Even When Data Are Sampled from a Population
.................................172
7.3.2
Point
1:
Nature Defines the Population, Not Vice Versa
........................172
7.3.3
Point
2:
The Population Is Not Well Defined
...........................................173
7.3.4
Point
3:
Population Conditional Distributions Are Discontinuous
......173
7.3.5
Point
4:
The Conditional Population Distribution p{y x) Does Not
Exist for Many
χ
...........................................................................................174
7.3.6
Point
5:
The Population Model Ignores Design and Measurement
Effects
............................................................................................................175
7.4
The Process Model versus the Population Model
................................................182
7.5
Independent and Identically Distributed Random Variables
and Other Models
.....................................................................................................133
7.6
Checking the iid Assumption
.................................................................................
1§7
Vocabulary and Formula Summaries
................................................................................195
Exercises
................................................................................................................................193
8.
Expected Value and the Law of Large Numbers
..........................................................201
8.1
Introduction
...............................................................................................................201
8.2
Discrete Case
.............................................................................................................201
8.3
Continuous Case
.......................................................................................................204
8.4
Law of Large Numbers
............................................................................................207
Contents ix
8.5
Law of Large Numbers for the Bernoulli Distribution
.......................................214
8.6
Keeping the Terminology Straight: Mean, Average, Sample Mean,
Sample Average, and Expected Value
....................................................................214
8.7
Bootstrap Distribution and the Plug-In Principle
................................................216
Vocabulary and Formula Summaries
................................................................................218
Exercises
................................................................................................................................220
9.
Functions of Random Variables: Their Distributions and Expected Values
.........223
9.1
Introduction
...............................................................................................................223
9.2
Distributions of Functions: The Discrete Case
.....................................................223
9.3
Distributions of Functions: The Continuous Case
...............................................225
9.4
Expected Values of Functions and the Law of the Unconscious Statistician...
227
9.5
Linearity and Additivity Properties
.......................................................................228
9.6
Nonlinear Functions and Jensen s Inequality
.......................................................231
9.7
Variance
......................................................................................................................235
9.8
Standard Deviation, Mean Absolute Deviation, and Chebyshev s
Inequality
..............................................................................................................239
9.9
Linearity Property of Variance
...............................................................................244
9.10
Skewness and Kurtosis
............................................................................................248
Vocabulary and Formula Summaries
................................................................................254
Exercises
................................................................................................................................256
10.
Distributions of Totals
......................................................................................................261
10.1
Introduction
...............................................................................................................261
10.2
Additivity Property of Variance
.............................................................................261
10.3
Covariance and Correlation
....................................................................................267
10.4
Central Limit Theorem
.............................................................................................272
Vocabulary and Formula Summaries
................................................................................277
Exercises
................................................................................................................................279
11.
Estimation: Unbiasedness, Consistency, and Efficiency
............................................283
11.1
Introduction
...............................................................................................................283
11.2
Biased and Unbiased Estimators
............................................................................284
11.3
Bias of the Plug-In Estimator of Variance
..............................................................287
11.4
Removing the Bias of the Plug-In Estimator of Variance
....................................292
11.5
The Joke Is on Us: The Standard Deviation Estimator Is Biased after All
........294
11.6
Consistency of Estimators
........................................................................................296
11.7
Efficiency of Estimators
............................................................................................298
Vocabulary and Formula Summaries
................................................................................303
Exercises
................................................................................................................................304
12.
Likelihood Function and Maximum Likelihood Estimates
......................................307
12.1
Introduction
...............................................................................................................307
12.2
Likelihood Function
.................................................................................................307
12.3
Maximum Likelihood Estimates
.............................................................................318
12.4 Wald
Standard Error
.................................................................................................334
Vocabulary and Formula Summaries
................................................................................337
Exercises
................................................................................................................................338
Contents
13. Bayesian
Statistics
..............................................................................................................343
13.1
Introduction:
Play
a
Game
with
Hans!
..................................................................343
13.2 Prior Information
and Posterior
Knowledge........................................................345
13.3
Case of the Unknown Survey.................................................................................
346
13.4
Bayesian Statistics: The Overview
..........................................................................349
13.5
Bayesian Analysis of the Bernoulli Parameter
.....................................................350
13.6
Bayesian Analysis Using Simulation
......................................................................356
13.7
What Good Is
Bayes?
................................................................................................359
Vocabulary and Formula Summaries
................................................................................368
Exercises
................................................................................................................................
14.
Frequentist Statistical Methods
.......................................................................................373
14.1
Introduction
...............................................................................................................373
14.2
Large-Sample Approximate Frequentist Confidence Interval
for the Process Mean
................................................................................................375
14.3
What Does Approximate Really Mean for an Interval Range?
............................381
14.4
Comparing the Bayesian and Frequentist Paradigms
.........................................384
Vocabulary and Formula Summaries
................................................................................386
Exercises
................................................................................................................................387
15.
Are Your Results Explainable by Chance Alone?
........................................................389
15.1
Introduction
...............................................................................................................389
15.2
What Does by Chance Alone Mean?
.........................................................................390
15.3
Thep-Value
.................................................................................................................395
15.4
The Extremely Ugly pv
< 0.05
Rule of Thumb
..................................................399
Vocabulary and Formula Summaries
................................................................................405
Exercises
................................................................................................................................407
16.
Chi-Squared, Student s t, and F-Distributions, with Applications
.........................411
16.1
Introduction
...............................................................................................................411
16.2
Linearity and Additivity Properties of the Normal Distribution
......................412
16.3
Effect of Using an Estimate of
σ
.............................................................................413
16.4
Chi-Squared Distribution
........................................................................................416
16.5
Frequentist Confidence Interval fora
....................................................................420
16.6
Student s
ŕ-Distribution
............................................................................................422
16.7
Comparing Two Independent Samples Using a Confidence Interval
...............426
16.8
Comparing Two Independent Homoscedastic Normal Samples via
Hypothesis Testing
...................................................................................................432
16.9
F-Distribution and ANOVA Test
.............................................................................435
16.10
F-Distribution and Comparing Variances of Two Independent Groups
..........441
Vocabulary and Formula Summaries
................................................................................444
Exercises
................................................................................................................................
44g
17.
Likelihood Ratio Tests
............................................................................................... 452
17.1
Introduction
........................................................................................ 452
17.2
Likelihood Ratio Method for Constructing Test Statistics
..................................452
17.3
Evaluating the Statistical Significance of Likelihood Ratio Test Statistics
.......467
Contents xi
17.4
Likelihood
Ratio Goodness-of-Fit Tests.................................................................474
17.5
Cross-Classification Frequency Tables and Tests of Independence
...................480
17.6
Comparing Non-Nested Models via the AIC Statistic
........................................483
Vocabulary and Formula Summaries
................................................................................485
Exercises
................................................................................................................................487
18.
Sample Size and Power
.....................................................................................................491
18.1
Introduction
...............................................................................................................491
18.2
Choosing a Sample Size for a Prespecified Accuracy Margin
...........................493
18.3
Power
..........................................................................................................................496
18.4
Noncentral
Distributions
.........................................................................................503
18.5
Choosing a Sample Size for Prespecified Power
..................................................506
18.6
Post Hoc Power: A Useless Statistic
........................................................................508
Vocabulary and Formula Summaries
................................................................................510
Exercises
................................................................................................................................511
19.
Robustness and Nonparametric Methods
.....................................................................515
19.1
Introduction
...............................................................................................................515
19.2
Nonparametric Tests Based on the Rank Transformation
..................................517
19.3
Randomization Tests
................................................................................................519
19.4
Level and Power Robustness
...................................................................................522
19.5
Bootstrap Percentile-r Confidence Interval
...........................................................526
Vocabulary and Formula Summaries
................................................................................530
Exercises
................................................................................................................................531
20.
Final Words
..........................................................................................................................533
Index
.............................................................................................................................................535
|
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| isbn | 9781466512108 |
| language | English |
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| series2 | Texts in statistical science A Chapman & Hall book |
| spelling | Westfall, Peter H. 1957- Verfasser (DE-588)171276752 aut Understanding advanced statistical methods Peter H. Westfal (Information Systems and Quantitative Sciences, Texas Tech University, USA), Kevin S. S. Henning (Department of Economics and International Business, Sam Houston State University, USA) Boca Raton CRC Press, Taylor & Francis Group 2013 xxv, 543 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Texts in statistical science A Chapman & Hall book Mathematical statistics Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Statistik (DE-588)4056995-0 s DE-604 Henning, Kevin S. S. Verfasser (DE-588)1048071499 aut Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027271096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Westfall, Peter H. 1957- Henning, Kevin S. S. Understanding advanced statistical methods Mathematical statistics Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4123623-3 |
| title | Understanding advanced statistical methods |
| title_auth | Understanding advanced statistical methods |
| title_exact_search | Understanding advanced statistical methods |
| title_full | Understanding advanced statistical methods Peter H. Westfal (Information Systems and Quantitative Sciences, Texas Tech University, USA), Kevin S. S. Henning (Department of Economics and International Business, Sam Houston State University, USA) |
| title_fullStr | Understanding advanced statistical methods Peter H. Westfal (Information Systems and Quantitative Sciences, Texas Tech University, USA), Kevin S. S. Henning (Department of Economics and International Business, Sam Houston State University, USA) |
| title_full_unstemmed | Understanding advanced statistical methods Peter H. Westfal (Information Systems and Quantitative Sciences, Texas Tech University, USA), Kevin S. S. Henning (Department of Economics and International Business, Sam Houston State University, USA) |
| title_short | Understanding advanced statistical methods |
| title_sort | understanding advanced statistical methods |
| topic | Mathematical statistics Statistik (DE-588)4056995-0 gnd |
| topic_facet | Mathematical statistics Statistik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027271096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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