Probability theory and statistical inference: empirical modeling with observational data
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York ; Melbourne ; New Delhi ; Singapore
Cambridge University Press
2019
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| Ausgabe: | Second edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xxi, 764 Seiten Diagramme |
| ISBN: | 9781107185142 9781316636374 |
Internformat
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| 245 | 1 | 0 | |a Probability theory and statistical inference |b empirical modeling with observational data |c Aris Spanos, Virginia Tech (Virginia Polytechnic Institute & State University) |
| 250 | |a Second edition | ||
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Datensatz im Suchindex
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| adam_text | Contents Preface to the Second Edition page xix 1 An Introduction to Empirical Modeling 1.1 Introduction 1.2 Stochastic Phenomena: A Preliminary View 1.2.1 Chance Regularity Patterns 1.2.2 From Chance Regularities to Probabilities 1.2.3 Chance Regularity Patterns and Real-World Phenomena 1.3 Chance Regularities and Statistical Models 1.4 Observed Data and Empirical Modeling 1.4.1 Experimental vs. Observational Data 1.4.2 Observed Data and the Nature of a Statistical Model 1.4.3 Measurement Scales and Data 1.4.4 Measurement Scale and Statistical Analysis 1.4.5 Cross-Section vs. Time Series, is that the Question? 1.4.6 Limitations of Economic Data 1.5 Statistical Adequacy 1.6 Statistical vs. Substantive Information* 1.7 Looking Ahead 1.8 Questions and Exercises 1 1 3 3 7 11 12 14 14 15 16 18 20 22 23 25 27 28 2 Probability Theory as a Modeling Framework 2.1 Introduction 2.1.1 Primary Objective 2.1.2 Descriptive vs. Inferential Statistics 2.2 Simple Statistical Model: A Preliminary View 2.2.1 The Basic Structure of a Simple Statistical Model 2.2.2 The Notion of a Random Variable: A Naive View 2.2.3 Density Functions 2.2.4 A Random Sample: A Preliminary View 2.3 Probability Theory: An Introduction 2.3.1 Outlining the Early Milestones of Probability Theory 2.3.2 Probability Theory: A Modeling Perspective 2.4 A Simple Generic Stochastic Mechanism 2.4.1 The Notion of a Random Experiment 2.4.2 A Bird’s-Eye View of the Unfolding Story 30 30 30 30 32 33 34 35 36 40 40 42 42 42 44 VII
viii Contents 2.5 2.6 2.7 2.8 2.9 3 Formalizing Condition fa]: The Outcomes Set 2.5.1 The Concept of a Set in Set Theory 2.5.2 The Outcomes Set 2.5.3 Special Types of Sets Formalizing Condition [b]: Events and Probabilities 2.6.1 Set-Theoretic Operations 2.6.2 Events vs. Outcomes 2.6.3 Event Space 2.6.4 A Digression: What is a Function? 2.6.5 The Mathematical Notion of Probability 2.6.6 Probability Space (S,a, P(.)) 2.6.7 Mathematical Deduction Conditional Probability and independence 2.7.1 Conditional Probability and its Properties 2.7.2 The Concept of Independence Among Events Formalizing Condition [c]: Sampling Space 2.8.1 The Concept of Random Trials 2.8.2 The Concept of a Statistical Space. 2.8.3 The Unfolding Story Ahead Questions and Exercises 45 45 45 46 48 48 51 51 58 59 63 64 65 65 69 70 70 72 74 75 The Concept of a Probability Model 78 3.1 78 78 79 80 81 3.2 3.3 3.4 3.5 3.6 3.7 Introduction 3.1.1 The Story So Far and What Comes Next The Concept of a Random Variable 3.2.1 The Case of a Finite Outcomes Set: S = {.51,ν2, ··· ,sn} 3.2.2 Key Features of a Random Variable 3.2.3 The Case of a Countable Outcomes Set: 5 = խւ,¿2....,sn,...} The General Concept of a Random Variable 3.3.1 The Case of an Uncountable Outcomes Set S Cumulative Distribution and Density Functions 3.4.1 The Concept of a Cumulative Distribution Function 3.4.2 The Concept of a Density Function From a Probability Space to a Probability Model 3.5.1 Parameters and Moments 3.5.2 Functions of a Random Variable 3.5.3 Numerical Characteristics of Random Variables 3.5.4 Higher Moments 3.5.5 The Problem of
Moments* 3.5.6 Other Numerical Characteristics Summary Questions and Exercises 85 86 86 89 89 91 95 97 97 99 102 110 112 118 119 Appendix 3.A: Univariate Distributions 121
Contents 3.A.1 3.A.2 Discrete Univariate Distributions Continuous Univariate Distributions ix 121 123 A Simple Statistical Model 4.1 Introduction 4.1.1 The Story So Far, a Summary 4.1.2 From Random Trials to a Random Sample: A First View 4.2 Joint Distributions of Random Variables 4.2.1 Joint Distributions of Discrete Random Variables 4.2.2 Joint Distributions of Continuous Random Variables 4.2.3 Joint Moments of Random Variables 4.2.4 The n Random Variables Joint Distribution 4.3 Marginal Distributions 4.4 Conditional Distributions 4.4.1 Conditional Probability 4.4.2 Conditional Density Functions 4.4.3 Continuous/Discrete Random Variables* 4.4.4 Conditional Moments 4.4.5 A Digression: Other Forms of Conditioning 4.4.6 Marginalization vs. Conditioning 4.4.7 Conditioning on Events vs. Random Variables 4.5 Independence 4.5.1 Independence in the Two Random Variable Case 4.5.2 Independence in the n Random Variable Case 4.6 Identical Distributions and Random Samples 4.6.1 Identically Distributed Random Variables 4.6.2 A Random Sample of Random Variables 4.7 Functions of Random Variables 4.7.1 Functions of One Random Variable 4.7.2 Functions of Several Random Variables 4.7.3 Ordered Sample and its Distributions* 4.8 A Simple Statistical Model 4.8.1 From a Random Experiment to a Simple Statistical Model 4.9 The Statistical Model in Empirical Modeling 4.9.1 The Concept of a Statistical Model: A Preliminary View 4.9.2 Statistical Identification of Parameters The Unfolding Story Ahead 4.9.3 Questions and Exercises 4.10 Appendix 4.A: Bivariate Distributions 4.A.1 Discrete Bivariate
Distributions 4.A.2 Continuous Bivariate Distributions 130 130 130 130 131 131 133 136 138 139 142 142 143 146 146 148 150 151 155 155 156 158 158 160 161 161 162 165 166 166 167 167 168 169 170 171 171 172 Chance Regularities and Probabilistic Concepts Introduction 5.1 176 176
x Contents 5.2 5.3 5.4 5.5 5.6 5.7 6 5.1.1 Early Developments in Graphical Techniques 5.1.2 Why Do We Care About Graphical Techniques? The t-Plot and Independence The t֊Plot and Homogeneity Assessing Distribution Assumptions 5.4.1 Data that Exhibit Dependence/Heterogeneity 5.4.2 Data that Exhibit Normal IID Chance Regularities 5.4.3 Data that Exhibit Non-Normal IID Regularities 5.4.4 The Histogram, the Density Function, and Smoothing 5.4.5 Smoothed Histograms and Non-Random Samples The Empirical CDF and Related Graphs* 5.5.1 The Concept of the Empirical cdf (ecdf) 5.5.2 Probability Plots 5.5.3 Empirical Example: Exchange Rate Data Summary Questions and Exercises Appendix 5.A: Data - Log-Returns Statistical Models and Dependence 6.1 Introduction 6.1.1 Extending a Simple Statistical Model 6.2 Non-Random Sample: A Preliminary View 6.2.1 Sequential Conditioning: Reducing the Dimensionality 6.2.2 Keeping ал Eye on the Forest! 6.3 Dependence and Joint Distributions 6.3.1 Dependence Between Two Random Variables 6.4 Dependence and Moments 6.4.1 Joint Moments and Dependence 6.4.2 Conditional Moments and Dependence 6.5 Joint Distributions and Modeling Dependence 6.5.1 Dependence and the Normal Distribution 6.5.2 A Graphical Display: The Scatterplot 6.5.3 Dependence and the Elliptically Symmetric Family 6.5.4 Dependence and Skewed Distributions 6.5.5 Dependence in the Presence of Heterogeneity 6.6 Modeling Dependence and Copulas* 6.7 Dependence for Categorical Variables 6.7.1 Measurement Scales and Dependence 6.7.2 Dependence and Ordinal Variables 6.7.3 Dependence and Nominal
Variables 6.8 Conditional Independence 6.8.1 The Multivariate Normal Distribution 6.8.2 The Multivariate Bernoulli Distribution 6.8.3 Dependence in Mixed (Discrete/Continuous) Variables 176 177 178 184 189 189 195 196 201 206 206 207 208 215 218 219 220 222 222 222 224 225 227 228 228 229 229 232 233 234 236 240 245 257 258 262 262 263 266 268 269 271 272
Contents 6.9 6.10 What Comes Next? Questions and Exercises XI 273 274 7 Regression Models 7.1 Introduction 7.2 Conditioning and Regression 7.2.1 Reduction and Conditional Moment Functions 7.2.2 Regression and Skedastic Functions 7.2.3 Selecting an Appropriate Regression Model 7.3 Weak Exogeneity and Stochastic Conditioning 7.3.1 The Concept of Weak Exogeneity 7.3.2 Conditioning on a σ-Field 7.3.3 Stochastic Conditional Expectation and its Properties 7.4 A Statistical Interpretation of Regression 7.4.1 The Statistical Generating Mechanism 7.4.2 Statistical vs. Substantive Models, Once Again 7.5 Regression Models and Heterogeneity 7.6 Summary and Conclusions 7.7 Questions and Exercises 277 277 279 279 281 288 292 292 295 297 301 301 304 308 310 312 8 Introduction to Stochastic Processes 8.1 Introduction 8.1.1 Random Variables and Orderings 8.2 The Concept of a Stochastic Process 8.2.1 Defining a Stochastic Process 8.2.2 Classifying Stochastic Processes; What a Mess! 8.2.3 Characterizing a Stochastic Process 8.2.4 Partial Sums and Associated Stochastic Processes 8.2.5 Gaussian (Normal) Process; A First View 8.3 Dependence Restrictions (Assumptions) 8.3.1 Distribution-Based Concepts of Dependence 8.3.2 Moment-Based Concepts of Dependence 8.4 Heterogeneity Restrictions (Assumptions) 8.4.1 Distribution-Based Heterogeneity Assumptions 8.4.2 Moment-Based Heterogeneity Assumptions 8.5 Building Block Stochastic Processes 8.5.1 IID Stochastic Processes 8.5.2 White-Noise Process 8.6 Markov and Related Stochastic Processes 8.6.1 Markov Process 8.6.2 Random Walk Processes 8.6.3
Martingale Processes 8.6.4 Martingale Difference Process 8.7 Gaussian Processes 315 315 316 318 318 320 322 324 328 329 329 330 331 331 333 335 335 336 336 336 338 340 342 345
Contents XII 8.8 8.9 8.10 9 8.7.1 AR(p) Process: Probabilistic Reduction Perspective 8.7.2 A Wiener Process and a Unit Root [UR(1)] Model 8.7.3 Moving Average [MA(g)] Process 8.7.4 Autoregressive vs. Moving Average Processes 8.7.5 The Brownian Motion Process* Counting Processes* 8.8.1 The Poisson Process 8.8.2 Duration (Hazard-Based) Models Summary and Conclusions Questions and Exercises Appendix 8.A: Asymptotic Dependence and Heterogeneity Assumptions* 8.A.1 Mixing Conditions 8.A.2 Ergodicity Limit Theorems in Probability 9.1 Introduction 9.1.1 Why Do We Care About Limit Theorems? 9.1.2 Terminology and Taxonomy 9.1.3 Popular Misconceptions About Limit Theorems 9.2 Tracing the Roots of Limit Theorems 9.2.1 Bernoulli’s Law of Large Numbers: A First View 9.2.2 Early Steps Toward the Central Limit Theorem 9.2.3 Ti e First SLLN 9.2.4 Probabilistic Convergence Modes: A First View 9.3 The WeMLew of Large Numbers 9.3.1 Pemoulli’s WLLN 9.3 2 Poisson’s WLLN 9.3.3 Chebyshev’s WLLN 9.3.4 Markov’s WLLN 9.3.5 Bernstein’s WLLN 9.3.6 Khinchin’s WLLN 9.4 The Strong Law of Large Numbers 9.4.1 Borel’s (1909) SLLN 9.4.2 Kolmogorov’s SLLN 9.4.3 SLLN for a Martingale 9.4.4 SLLN for a Stationary Process 9.4.5 The Law of Iterated Logarithm* 9.5 The Central Limit Theorem 9.5.1 De Moivre-Laplace CLT 9.5.2 Lyapunov’s CLT 9.5.3 Lindeberg-Feller’s CLT 9.5.4 Chebyshev’s CLT 9.5.5 Hajek-Sidak CLT 345 349 352 353 354 360 361 363 364 367 369 369 370 373 373 374 375 376 377 377 378 381 381 383 383 385 386 387 388 389 390 390 391 392 394 395 396 397 399 399 401 401
Contente 9.6 9.7 9.8 10 9.5.6 CLT for a Martingale 9.5.7 CLT for a Stationary Process 9.5.8 The Accuracy of the Normal Approximation 9.5.9 Stable and Other Limit Distributions* Extending the Limit Theorems* 9.6.1 A Uniform SLLN* Summary and Conclusions Questions and Exercises Appendix 9.A: Probabilistic Inequalities 9.A.1 Probability 9. A.2 Expectation Appendix 9.B: Functional Central Limit Theorem From Probability Theory to Statistical Inference 10.1 Introduction 10.2 Mathematical Probability՛. A Brief Summary 10.2.1 Kolmogorov’s Axiomatic Approach 10.2.2 Random Variables and Statistical Models 10.3 Frequentisi Interpretation(s) of Probability 10.3.1 “Randomness” (Stochasticity) is a Feature of the Real World 10.3.2 Model-Based Frequentisi Interpretation of Probability 10.3.3 Von Mises’ Frequentisi Interpretation of Probability 10.3.4 Criticisms Leveled Against the Frequentisi Interpretation 10.3.5 Kolmogorov Complexity: An Algorithmic Perspective 10.3.6 The Propensity Interpretation of Probability 10.4 Degree of Belief Interpretation(s) of Probability 10.4.1 “Randomness” is in the Mind of the Beholder 10.4.2 Degrees of Subjective Belief 10.4.3 Degrees of “Objective Belief”: Logical Probability 10.4.4 Which Interpretation of Probability? 10.5 Frequentisi vs. Bayesian Statistical Inference 10.5.1 The Frequentisi Approach to Statistical Inference 10.5.2 The Bayesian Approach to Statistical Inference 10.5.3 Cautionary Notes on Misleading Bayesian Claims 10.6 An Introduction to Frequentisi Inference 10.6.1 Fisher and Neglected Aspects of Frequentisi Statistics 10.6.2 Basic
Frequentisi Concepts and Distinctions 10.6.3 Estimation: Point and Interval 10.6.4 Hypothesis Testing: A First View 10.6.5 Prediction (Forecasting) 10.6.6 Probability vs. Frequencies: The Empirical CDF 10.7 Non-Parametric Inference 10.7.1 Parametric vs. Non-Parametric Inference xiii 402 402 403 404 406 409 409 410 412 412 413 414 421 421 422 422 422 423 423 424 426 427 430 431 432 432 432 435 436 436 436 440 443 444 444 446 447 449 450 450 453 453
XIV Contents 10.8 10.9 10.10 11 12 10.7.2 Are Weaker Assumptions Preferable to Stronger Ones? 10.7.3 Induction vs. Deduction 10.7.4 Revisiting Generic Robustness Claims 10.7.5 Inference Based on Asymptotic Bounds 10.7.6 Whither Non-Parametric Modeling? The Basic Bootstrap Method 10.8.1 Bootstrapping and Statistical Adequacy Summary and Conclusions Questions and Exercises 454 457 458 458 460 461 462 464 466 Estimation I: Properties of Estimators 469 11.1 11.2 11.3 11.4 Introduction What is an Estimator? Sampling Distributions of Estimators Finite Sample Properties of Estimators 11.4.1 Unbiasedness 11.4.2 Efficiency: Relative vs. Full Efficiency 11.4.3 Sufficiency 11.4.4 Minimum MSE Estimators and Admissibility 11.5 Asymptotic Properties of Estimators 11.5.1 Consistency (Weak) 11.5.2 Consistency (Strong) 11.5.3 Asymptotic Normality 11.5.4 Asymptotic Efficiency 11.5.5 Properties of Estimators Beyond the First Two Moments 11.6 The Simple Normal Model: Estimation 11.7 Confidence Intervals (Interval Estimation) 11.7.1 Long-Run “Interpretation” of CIs 11.7.2 Constructing a Confidence Interval 11.7.3 Optimality of Confidence Intervals 11.8 Bayesian Estimation 11.8.1 Optimal Bayesian Rules 11.8.2 Bayesian Credible Intervals 11.9 Summary and Conclusions 11.10 Questions and Exercises 469 469 472 474 474 475 480 485 488 488 490 490 491 492 493 498 499 499 501 502 503 504 505 507 Estimation II: Methods of Estimation 510 12.1 12.2 510 511 511 514 517 519 524 Introduction The Maximum Likelihood Method 12.2.1 The Likelihood Function 12.2.2 Maximum Likelihood Estimators 12.2.3 The Score
Function 12.2.4 Two-Parameter Statistical Model 12.2.5 Properties of Maximum Likelihood Estimators
Contents 12.3 12.4 12.5 12.6 12.7 13 12.2.6 The Maximum Likelihood Method and its Crítics The Least-Squares Method 12.3.1 The Mathematical Principle of Least Squares 12.3.2 Least Squares as a Statistical Method Moment Matching Principle 12.4.1 Sample Moments and their Properties The Method of Moments 12.5.1 Karl Pearson’s Method of Moments 12.5.2 The Parametric Method of Moments 12.5.3 Properties of PMM Estimators Summary and Conclusions Questions and Exercises Appendix 12.A: Karl Pearson’s Approach Hypothesis Testing 13.1 Introduction 13.1.1 Difficulties in Mastering Statistical Testing 13.2 Statistical Testing Before R. A. Fisher 13.2.1 Francis Edgeworth’s Testing 13.2.2 Karl Pearson’s Testing 13.3 Fisher’s Significance Testing 13.3.1 A Closer Look at the p-value 13.3.2 R. A. Fisher and Experimental Design 13.3.3 Significance Testing: Empirical Examples 13.3.4 Summary of Fisher’s Significance Testing 13.4 Neyman-Pearson Testing 13.4.1 N-P Objective: Improving Fisher’s Significance Testing 13.4.2 Modifying Fisher’s Testing Framing: A First View 13.4.3 A Historical Excursion 13.4.4 The Archetypal N-P Testing Framing 13.4.5 Significance Level a vs. the p֊value 13.4.6 Optimality of a Neyman-Pearson Test 13.4.7 Constructing Optimal Tests: The N-P Lemma 13.4.8 Extending the Neyman-Pearson Lemma 13.4.9 Constructing Optimal Tests: Likelihood Ratio 13.4.10 Bayesian Testing Using the Bayes Factor 13.5 Error-Statistical Framing of StatisticalTesting 13.5.1 N-P Testing Driven by Substantively Relevant Values 13.5.2 Foundational Issues Pertaining to Statistical Testing 13.5.3 Post-
Data Severity Evaluation: An Evidential Account 13.5.4 Revisiting Issues Bedeviling Frequentisi Testing 13.5.5 The Replication Crises and Severity 13.6 Confidence Intervals and their Optimality 13.6.1 Mathematical Duality Between Testing and CIs XV 532 534 534 535 536 539 543 543 544 546 547 549 551 553 553 553 555 555 556 558 561 563 565 568 569 569 570 574 575 578 580 586 588 591 594 596 596 598 600 603 609 610 610
XVI Contents 13.6.2 Uniformly Most Accurate CIs 13.6.3 Confidence Intervals vs. Hypothesis Testing 13.6.4 Observed Confidence Intervals and Severity 13.6.5 Fallacious Arguments for Using CIs Summary and Conclusions Questions and Exercises Appendix 13-А: Testing Differences Between Means 13.A.1 Testing the Difference Between Two Means 13.A.2 What Happens when Var{X ,) փ- №ւր(ճշէ)7 13.A.3 Bivariate Normal Model: Paired Sample Tests 13.A.4 Testing the Difference Between Two Proportions 13.A.5 One-Way Analysis of Variance 612 613 614 614 615 617 620 620 621 622 623 624 Linear Regression and Related Models І4Л Introduction 14.1.1 What is a Statistical Model? 14.2 Normal., Linear Regression Model 14.2.1 Specification 14.2.2 Estimation 14.2.3 Fitted Values and Residuals 14.2.4 Goodness-of-Fit Measures 14.2.5 Confidence Intervals and Hypothesis Testing 14.2.6 Normality and the LR Model 14.2.7 Testing a Substantive Model Against the Data Linear Regression and Least Squares 14.3 14,3.1 Mathematical Approximation and Statistical Curve-Fitting 14.3.2 Gauss-Markov Theorem 14.3.3 Asymptotic Properties of OLS Estimators Regression-Like Statistical Models 14.4 14.4.1 Gauss Linear Model 14.4.2 The Logit and Probit Models 14.4.3 The Poisson Regression-Like Model 14.4.4 Generalized Linear Models 14.4.5 The Gamma Regression-Like Model Multiple Linear Regression Model 14.5 14.5.1 Estimation 14.5.2 Linear Regression: Matrix Formulation 14.5.3 Fitted Values and Residuals 14.5.4 OLS Estimators and their Sampling Distributions The LR Model: Numerical Issues and Problems 14.6 14.6.1 The Problem of
Near-Collinearity 14.6.2 The Hat Matrix and Influential Observations 14.6.3 Individual Observation Influence Measures 625 625 625 626 626 628 633 635 635 642 643 648 13.7 13.8 14 648 651 653 655 655 655 657 657 658 658 660 661 662 665 666 666 673 674
Contents 14.7 14.8 15 xvii Conclusions Questions and Exercises Appendix 14.A: Generalized Linear Models 14.A. 1Exponential Family of Distributions 14. A.2 Common Features of Generalized Linear Models 14.A.3 MLE and the Exponential Family Appendix 14.B: Data 675 677 680 680 681 682 683 Misspecification (M-S) Testing 15.1 Introduction 15.2 Misspecification and Inference: A First View 15.2.1 Actual vs. Nominal Error Probabilities 15.2.2 Reluctance to Test the Validity of Model Assumptions 15.3 Non-Parametric (Omnibus) M-S Tests 15.3.1 The Runs M-S Test for the IID Assumptions [2]-[4] 15.3.2 Kolmogorov’s M-S Test for Normality ([1]) 15.4 Parametric (Directional) M-S Testing 15.4.1 A Parametric M-S Test for Independence ([4]) 15.4.2 Testing Independence and Mean Constancy ([2] and [4]) 15.4.3 Testing Independence and Variance Constancy ([2] and [4]) 15.4.4 The Skewness-Kurtosis Test of Normality 15.4.5 Simple Normal Model: A Summary of M-S Testing 15.5 Misspecification Testing: A Formalization 15.5.1 Placing M-S Testing in a Proper Context 15.5.2 Securing the Effectiveness/Reliability of M-S Testing 15.5.3 M-S Testing and the Linear Regression Model 15.5.4 The Multiple Testing (Comparisons) Issue 15.5.5 Testing for r-Invariance of the Parameters 15.5.6 Where do Auxiliary Regressions Come From? 15.5.7 M-S Testing for Logit/Probit Models 15.5.8 Revisiting Yule’s “Nonsense Correlations” 15.5.9 Respecification 15.6 An Illustration of Empirical Modeling 15.6.1 The Traditional Curve-Fitting Perspective 15.6.2 Traditional ad hoc M-S Testing and Respecification 15.6.3 The Probabilistic
Reduction Approach 15.7 Summary and Conclusions 15.8 Questions and Exercises Appendix 15.A: Data 685 685 688 688 691 694 694 695 697 697 698 References Index 700 700 701 703 703 704 705 706 707 707 710 710 713 716 716 718 721 729 731 734 736 752
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| any_adam_object | 1 |
| author | Spanos, Aris 1952- |
| author_GND | (DE-588)170170624 |
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| dewey-full | 330.015195 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 330 - Economics |
| dewey-raw | 330.015195 |
| dewey-search | 330.015195 |
| dewey-sort | 3330.015195 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| edition | Second edition |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV045881528 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:29:17Z |
| institution | BVB |
| isbn | 9781107185142 9781316636374 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031264686 |
| oclc_num | 1124727943 |
| open_access_boolean | |
| owner | DE-11 DE-521 DE-634 DE-19 DE-BY-UBM DE-355 DE-BY-UBR |
| owner_facet | DE-11 DE-521 DE-634 DE-19 DE-BY-UBM DE-355 DE-BY-UBR |
| physical | xxi, 764 Seiten Diagramme |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Spanos, Aris 1952- Verfasser (DE-588)170170624 aut Probability theory and statistical inference empirical modeling with observational data Aris Spanos, Virginia Tech (Virginia Polytechnic Institute & State University) Second edition Cambridge ; New York ; Melbourne ; New Delhi ; Singapore Cambridge University Press 2019 xxi, 764 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Inferenzstatistik (DE-588)4247120-5 gnd rswk-swf Ökonometrie (DE-588)4132280-0 gnd rswk-swf Statistische Entscheidungstheorie (DE-588)4077850-2 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Inferenzstatistik (DE-588)4247120-5 s DE-188 Ökonometrie (DE-588)4132280-0 s Statistische Entscheidungstheorie (DE-588)4077850-2 s 1\p 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=031264686&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Spanos, Aris 1952- Probability theory and statistical inference empirical modeling with observational data Inferenzstatistik (DE-588)4247120-5 gnd Ökonometrie (DE-588)4132280-0 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4247120-5 (DE-588)4132280-0 (DE-588)4077850-2 (DE-588)4079013-7 (DE-588)4123623-3 |
| title | Probability theory and statistical inference empirical modeling with observational data |
| title_auth | Probability theory and statistical inference empirical modeling with observational data |
| title_exact_search | Probability theory and statistical inference empirical modeling with observational data |
| title_full | Probability theory and statistical inference empirical modeling with observational data Aris Spanos, Virginia Tech (Virginia Polytechnic Institute & State University) |
| title_fullStr | Probability theory and statistical inference empirical modeling with observational data Aris Spanos, Virginia Tech (Virginia Polytechnic Institute & State University) |
| title_full_unstemmed | Probability theory and statistical inference empirical modeling with observational data Aris Spanos, Virginia Tech (Virginia Polytechnic Institute & State University) |
| title_short | Probability theory and statistical inference |
| title_sort | probability theory and statistical inference empirical modeling with observational data |
| title_sub | empirical modeling with observational data |
| topic | Inferenzstatistik (DE-588)4247120-5 gnd Ökonometrie (DE-588)4132280-0 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Inferenzstatistik Ökonometrie Statistische Entscheidungstheorie Wahrscheinlichkeitstheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031264686&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT spanosaris probabilitytheoryandstatisticalinferenceempiricalmodelingwithobservationaldata |