Mathematical statistics and data analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Belmont, Calif.
Thomson Brooks/Cole
2007
|
| Edition: | 3. ed., internat. student ed. |
| Series: | Duxbury advanced series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 603, 63 S. graph. Darst. |
| ISBN: | 0534399428 0495110892 9780495110897 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Mathematical statistics and data analysis
Autor: Rice, John A.
Jahr: 2007
Contents
2.2.3 The Normal Distribution 54
2.2.4 The Beta Density 58
2.3 Functions of a Random Variable 58
2.4 Concluding Remarks 64
2.5 Problems 64
3 Joint Distributions 71
3.1 Introduction 71
3.2 Discrete Random Variables 72
3.3 Continuous Random Variables 75
3.4 Independent Random Variables 84
3.5 Conditional Distributions 87
3.5.1 The Discrete Case 87
3.5.2 The Continuous Case 88
3.6 Functions of Jointly Distributed Random Variables 96
3.6.1 Sums and Quotients 96
3.6.2 The General Case 99
3.7 Extrema and Order Statistics 104
3.8 Problems 107
4 Expected Values 116
4.1 The Expected Value of a Random Variable 116
4.1.1 Expectations of Functions of Random Variables 121
4.1.2 Expectations of Linear Combinations of Random Variables 124
4.2 Variance and Standard Deviation 130
4.2.1 A Model for Measurement Error 135
4.3 Covariance and Correlation 138
4.4 Conditional Expectation and Prediction 147
4.4.1 Definitions and Examples 147
4.4.2 Prediction 152
4.5 The Moment-Generating Function 155
4.6 Approximate Methods 161
4.7 Problems 166
vi Contents
5 Limit Theorems 177
5.1 Introduction 177
5.2 The Law of Large Numbers 177
5.3 Convergence in Distribution and the Central Limit Theorem 181
5.4 Problems 188
6 Distributions Derived from the Normal Distribution 192
6.1 Introduction 192
6.2 x2, f, and F Distributions 192
6.3 The Sample Mean and the Sample Variance 195
6.4 Problems 198
7 Survey Sampling 199
7.1 Introduction 199
7.2 Population Parameters 200
7.3 Simple Random Sampling 202
7.3.1 The Expectation and Variance of the Sample Mean 203
7.3.2 Estimation of the Population Variance 210
7.3.3 The Normal Approximation to the Sampling Distribution of X 214
7.4 Estimation of a Ratio 220
7.5 Stratified Random Sampling 227
7.5.1 Introduction and Notation 227
7.5.2 Properties of Stratified Estimates 228
7.5.3 Methods of Allocation 232
7.6 Concluding Remarks 238
7.7 Problems 239
8 Estimation of Parameters and Fitting of Probability Distributions 255
8.1 Introduction 255
8.2 Fitting the Poisson Distribution to Emissions of Alpha Particles 255
8.3 Parameter Estimation 257
8.4 The Method of Moments 260
8.5 The Method of Maximum Likelihood 267
Contents vii
8.5.1 Maximum Likelihood Estimates of Multinomial Cell Probabilities 272
8.5.2 Large Sample Theory for Maximum Likelihood Estimates 274
8.5.3 Confidence Intervals from Maximum Likelihood Estimates 279
8.6 The Bayesian Approach to Parameter Estimation 285
8.6.1 Further Remarks on Priors 294
8.6.2 Large Sample Normal Approximation to the Posterior 296
8.6.3 Computational Aspects 297
8.7 Efficiency and the Cramér-Rao Lower Bound 298
8.7.1 An Example: The Negative Binomial Distribution 302
8.8 Sufficiency 305
8.8.1 A Factorization Theorem 306
8.8.2 The Rao-Blackwell Theorem 310
8.9 Concluding Remarks 311
8.10 Problems 312
9 Testing Hypotheses and Assessing Goodness of Fit 329
9.1 Introduction 329
9.2 The Neyman-Pearson Paradigm 331
9.2.1 Specification of the Significance Level and the Concept of a p-value 334
9.2.2 The Null Hypothesis 335
9.2.3 Uniformly Most Powerful Tests 336
9.3 The Duality of Confidence Intervals and Hypothesis Tests 337
9.4 Generalized Likelihood Ratio Tests 339
9.5 Likelihood Ratio Tests for the Multinomial Distribution 341
9.6 The Poisson Dispersion Test 347
9.7 Hanging Rootograms 349
9.8 Probability Plots 352
9.9 Tests for Normality 358
9.10 Concluding Remarks 361
9.11 Problems 362
10 Summarizing Data 377
10.1 Introduction 377
10.2 Methods Based on the Cumulative Distribution Function 378
viii Contents
10.2.1 The Empirical Cumulative Distribution Function 378
10.2.2 The Survival Function 380
10.2.3 Quantile-Quantile Plots 385
10.3 Histograms, Density Curves, and Stem-and-Leaf Plots 389
10.4 Measures of Location 392
10.4.1 The Arithmetic Mean 393
10.4.2 The Median 395
10.4.3 The Trimmed Mean 397
10.4.4 M Estimates 397
10.4.5 Comparison of Location Estimates 398
10.4.6 Estimating Variability of Location Estimates by the Bootstrap 399
10.5 Measures of Dispersion 401
10.6 Boxplots 402
10.7 Exploring Relationships with Scatterplots 404
10.8 Concluding Remarks 407
10.9 Problems 408
11 Comparing Two Samples 420
11.1 Introduction 420
11.2 Comparing Two Independent Samples 421
11.2.1 Methods Based on the Normal Distribution 421
11.2.2 Power 433
11.2.3 A Nonparametric Method—The Mann-Whitney Test 435
11.2.4 Bayesian Approach 443
11.3 Comparing Paired Samples 444
11.3.1 Methods Based on the Normal Distribution 446
11.3.2 A Nonparametric Method—The Signed Rank Test 448
11.3.3 An Example—Measuring Mercury Levels in Fish 450
11.4 Experimental Design 452
11.4.1 Mammary Artery Ligation 452
11.4.2 The Placebo Effect 453
11.4.3 The Lanarkshire Milk Experiment 453
11.4.4 The Portacaval Shunt 454
11.4.5 FD CRedNo.40 455
11.4.6 Further Remarks on Randomization 456
Contents ix
11.4.7 Observational Studies, Confounding, and Bias in Graduate Admissions 457
11.4.8 Fishing Expeditions 458
11.5 Concluding Remarks 459
11.6 Problems 459
12 The Analysis of Variance 477
12.1 Introduction 477
12.2 The One-Way Layout 477
12.2.1 Normal Theory; the F Test 478
12.2.2 The Problem of Multiple Comparisons 485
12.2.3 A Nonparametric Method—The Kruskal-Wallis Test 488
12.3 The Two-Way Layout 489
12.3.1 Additive Parametrization 489
12.3.2 Normal Theory for the Two-Way Layout 492
12.3.3 Randomized Block Designs 500
12.3.4 A Nonparametric Method—Friedman s Test 503
12.4 Concluding Remarks 504
12.5 Problems 505
13 The Analysis of Categorical Data 514
13.1 Introduction 514
13.2 Fisher s Exact Test 514
13.3 The Chi-Square Test of Homogeneity 516
13.4 The Chi-Square Test of Independence 520
13.5 Matched-Pairs Designs 523
13.6 Odds Ratios 526
13.7 Concluding Remarks 530
13.8 Problems 530
14 Linear Least Squares 542
14.1 Introduction 542
14.2 Simple Linear Regression 547
14.2.1 Statistical Properties of the Estimated Slope and Intercept 547
Contents
14.2.2 Assessing the Fit 550
14.2.3 Correlation and Regression 560
14.3 The Matrix Approach to Linear Least Squares 564
14.4 Statistical Properties of Least Squares Estimates 567
14.4.1 Vector-Valued Random Variables 567
14.4.2 Mean and Covariance of Least Squares Estimates 573
14.4.3 Estimation of a2 575
14.4.4 Residuals and Standardized Residuals 576
14.4.5 Inference about ß 577
14.5 Multiple Linear Regression—An Example 580
14.6 Conditional Inference, Unconditional Inference, and the Bootstrap 585
14.7 Local Linear Smoothing 587
14.8 Concluding Remarks 591
14.9 Problems 591
Appendix A Common Distributions Al
Appendix B Tables A4
Bibliography A25
Answers to Selected Problems A32
Author Index A48
Applications Index A51
Subject Index A54
|
| adam_txt |
Titel: Mathematical statistics and data analysis
Autor: Rice, John A.
Jahr: 2007
Contents
2.2.3 The Normal Distribution 54
2.2.4 The Beta Density 58
2.3 Functions of a Random Variable 58
2.4 Concluding Remarks 64
2.5 Problems 64
3 Joint Distributions 71
3.1 Introduction 71
3.2 Discrete Random Variables 72
3.3 Continuous Random Variables 75
3.4 Independent Random Variables 84
3.5 Conditional Distributions 87
3.5.1 The Discrete Case 87
3.5.2 The Continuous Case 88
3.6 Functions of Jointly Distributed Random Variables 96
3.6.1 Sums and Quotients 96
3.6.2 The General Case 99
3.7 Extrema and Order Statistics 104
3.8 Problems 107
4 Expected Values 116
4.1 The Expected Value of a Random Variable 116
4.1.1 Expectations of Functions of Random Variables 121
4.1.2 Expectations of Linear Combinations of Random Variables 124
4.2 Variance and Standard Deviation 130
4.2.1 A Model for Measurement Error 135
4.3 Covariance and Correlation 138
4.4 Conditional Expectation and Prediction 147
4.4.1 Definitions and Examples 147
4.4.2 Prediction 152
4.5 The Moment-Generating Function 155
4.6 Approximate Methods 161
4.7 Problems 166
vi Contents
5 Limit Theorems 177
5.1 Introduction 177
5.2 The Law of Large Numbers 177
5.3 Convergence in Distribution and the Central Limit Theorem 181
5.4 Problems 188
6 Distributions Derived from the Normal Distribution 192
6.1 Introduction 192
6.2 x2, f, and F Distributions 192
6.3 The Sample Mean and the Sample Variance 195
6.4 Problems 198
7 Survey Sampling 199
7.1 Introduction 199
7.2 Population Parameters 200
7.3 Simple Random Sampling 202
7.3.1 The Expectation and Variance of the Sample Mean 203
7.3.2 Estimation of the Population Variance 210
7.3.3 The Normal Approximation to the Sampling Distribution of X 214
7.4 Estimation of a Ratio 220
7.5 Stratified Random Sampling 227
7.5.1 Introduction and Notation 227
7.5.2 Properties of Stratified Estimates 228
7.5.3 Methods of Allocation 232
7.6 Concluding Remarks 238
7.7 Problems 239
8 Estimation of Parameters and Fitting of Probability Distributions 255
8.1 Introduction 255
8.2 Fitting the Poisson Distribution to Emissions of Alpha Particles 255
8.3 Parameter Estimation 257
8.4 The Method of Moments 260
8.5 The Method of Maximum Likelihood 267
Contents vii
8.5.1 Maximum Likelihood Estimates of Multinomial Cell Probabilities 272
8.5.2 Large Sample Theory for Maximum Likelihood Estimates 274
8.5.3 Confidence Intervals from Maximum Likelihood Estimates 279
8.6 The Bayesian Approach to Parameter Estimation 285
8.6.1 Further Remarks on Priors 294
8.6.2 Large Sample Normal Approximation to the Posterior 296
8.6.3 Computational Aspects 297
8.7 Efficiency and the Cramér-Rao Lower Bound 298
8.7.1 An Example: The Negative Binomial Distribution 302
8.8 Sufficiency 305
8.8.1 A Factorization Theorem 306
8.8.2 The Rao-Blackwell Theorem 310
8.9 Concluding Remarks 311
8.10 Problems 312
9 Testing Hypotheses and Assessing Goodness of Fit 329
9.1 Introduction 329
9.2 The Neyman-Pearson Paradigm 331
9.2.1 Specification of the Significance Level and the Concept of a p-value 334
9.2.2 The Null Hypothesis 335
9.2.3 Uniformly Most Powerful Tests 336
9.3 The Duality of Confidence Intervals and Hypothesis Tests 337
9.4 Generalized Likelihood Ratio Tests 339
9.5 Likelihood Ratio Tests for the Multinomial Distribution 341
9.6 The Poisson Dispersion Test 347
9.7 Hanging Rootograms 349
9.8 Probability Plots 352
9.9 Tests for Normality 358
9.10 Concluding Remarks 361
9.11 Problems 362
10 Summarizing Data 377
10.1 Introduction 377
10.2 Methods Based on the Cumulative Distribution Function 378
viii Contents
10.2.1 The Empirical Cumulative Distribution Function 378
10.2.2 The Survival Function 380
10.2.3 Quantile-Quantile Plots 385
10.3 Histograms, Density Curves, and Stem-and-Leaf Plots 389
10.4 Measures of Location 392
10.4.1 The Arithmetic Mean 393
10.4.2 The Median 395
10.4.3 The Trimmed Mean 397
10.4.4 M Estimates 397
10.4.5 Comparison of Location Estimates 398
10.4.6 Estimating Variability of Location Estimates by the Bootstrap 399
10.5 Measures of Dispersion 401
10.6 Boxplots 402
10.7 Exploring Relationships with Scatterplots 404
10.8 Concluding Remarks 407
10.9 Problems 408
11 Comparing Two Samples 420
11.1 Introduction 420
11.2 Comparing Two Independent Samples 421
11.2.1 Methods Based on the Normal Distribution 421
11.2.2 Power 433
11.2.3 A Nonparametric Method—The Mann-Whitney Test 435
11.2.4 Bayesian Approach 443
11.3 Comparing Paired Samples 444
11.3.1 Methods Based on the Normal Distribution 446
11.3.2 A Nonparametric Method—The Signed Rank Test 448
11.3.3 An Example—Measuring Mercury Levels in Fish 450
11.4 Experimental Design 452
11.4.1 Mammary Artery Ligation 452
11.4.2 The Placebo Effect 453
11.4.3 The Lanarkshire Milk Experiment 453
11.4.4 The Portacaval Shunt 454
11.4.5 FD CRedNo.40 455
11.4.6 Further Remarks on Randomization 456
Contents ix
11.4.7 Observational Studies, Confounding, and Bias in Graduate Admissions 457
11.4.8 Fishing Expeditions 458
11.5 Concluding Remarks 459
11.6 Problems 459
12 The Analysis of Variance 477
12.1 Introduction 477
12.2 The One-Way Layout 477
12.2.1 Normal Theory; the F Test 478
12.2.2 The Problem of Multiple Comparisons 485
12.2.3 A Nonparametric Method—The Kruskal-Wallis Test 488
12.3 The Two-Way Layout 489
12.3.1 Additive Parametrization 489
12.3.2 Normal Theory for the Two-Way Layout 492
12.3.3 Randomized Block Designs 500
12.3.4 A Nonparametric Method—Friedman's Test 503
12.4 Concluding Remarks 504
12.5 Problems 505
13 The Analysis of Categorical Data 514
13.1 Introduction 514
13.2 Fisher's Exact Test 514
13.3 The Chi-Square Test of Homogeneity 516
13.4 The Chi-Square Test of Independence 520
13.5 Matched-Pairs Designs 523
13.6 Odds Ratios 526
13.7 Concluding Remarks 530
13.8 Problems 530
14 Linear Least Squares 542
14.1 Introduction 542
14.2 Simple Linear Regression 547
14.2.1 Statistical Properties of the Estimated Slope and Intercept 547
Contents
14.2.2 Assessing the Fit 550
14.2.3 Correlation and Regression 560
14.3 The Matrix Approach to Linear Least Squares 564
14.4 Statistical Properties of Least Squares Estimates 567
14.4.1 Vector-Valued Random Variables 567
14.4.2 Mean and Covariance of Least Squares Estimates 573
14.4.3 Estimation of a2 575
14.4.4 Residuals and Standardized Residuals 576
14.4.5 Inference about ß 577
14.5 Multiple Linear Regression—An Example 580
14.6 Conditional Inference, Unconditional Inference, and the Bootstrap 585
14.7 Local Linear Smoothing 587
14.8 Concluding Remarks 591
14.9 Problems 591
Appendix A Common Distributions Al
Appendix B Tables A4
Bibliography A25
Answers to Selected Problems A32
Author Index A48
Applications Index A51
Subject Index A54 |
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| genre | 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4143389-0 Aufgabensammlung gnd-content 3\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Einführung Aufgabensammlung Lehrbuch |
| id | DE-604.BV022879896 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:50:09Z |
| indexdate | 2024-07-09T21:07:36Z |
| institution | BVB |
| isbn | 0534399428 0495110892 9780495110897 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016084888 |
| oclc_num | 315216152 |
| open_access_boolean | |
| owner | DE-29T DE-11 |
| owner_facet | DE-29T DE-11 |
| physical | XVI, 603, 63 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Thomson Brooks/Cole |
| record_format | marc |
| series2 | Duxbury advanced series |
| spelling | Rice, John A. Verfasser aut Mathematical statistics and data analysis John A. Rice 3. ed., internat. student ed. Belmont, Calif. Thomson Brooks/Cole 2007 XVI, 603, 63 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Duxbury advanced series Erwartungswert (DE-588)4152930-3 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Statistischer Test (DE-588)4077852-6 gnd rswk-swf Stichprobe (DE-588)4057502-0 gnd rswk-swf Parameterschätzung (DE-588)4044614-1 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4143389-0 Aufgabensammlung gnd-content 3\p (DE-588)4123623-3 Lehrbuch gnd-content Datenanalyse (DE-588)4123037-1 s Statistik (DE-588)4056995-0 s Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s Parameterschätzung (DE-588)4044614-1 s Erwartungswert (DE-588)4152930-3 s 4\p DE-604 Stichprobe (DE-588)4057502-0 s Statistischer Test (DE-588)4077852-6 s 5\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016084888&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rice, John A. Mathematical statistics and data analysis Erwartungswert (DE-588)4152930-3 gnd Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Datenanalyse (DE-588)4123037-1 gnd Statistischer Test (DE-588)4077852-6 gnd Stichprobe (DE-588)4057502-0 gnd Parameterschätzung (DE-588)4044614-1 gnd |
| subject_GND | (DE-588)4152930-3 (DE-588)4056995-0 (DE-588)4121894-2 (DE-588)4123037-1 (DE-588)4077852-6 (DE-588)4057502-0 (DE-588)4044614-1 (DE-588)4151278-9 (DE-588)4143389-0 (DE-588)4123623-3 |
| title | Mathematical statistics and data analysis |
| title_auth | Mathematical statistics and data analysis |
| title_exact_search | Mathematical statistics and data analysis |
| title_exact_search_txtP | Mathematical statistics and data analysis |
| title_full | Mathematical statistics and data analysis John A. Rice |
| title_fullStr | Mathematical statistics and data analysis John A. Rice |
| title_full_unstemmed | Mathematical statistics and data analysis John A. Rice |
| title_short | Mathematical statistics and data analysis |
| title_sort | mathematical statistics and data analysis |
| topic | Erwartungswert (DE-588)4152930-3 gnd Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Datenanalyse (DE-588)4123037-1 gnd Statistischer Test (DE-588)4077852-6 gnd Stichprobe (DE-588)4057502-0 gnd Parameterschätzung (DE-588)4044614-1 gnd |
| topic_facet | Erwartungswert Statistik Wahrscheinlichkeitsverteilung Datenanalyse Statistischer Test Stichprobe Parameterschätzung Einführung Aufgabensammlung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016084888&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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