Mathematical Statistics for Economics and Business - Taschenbuch

EAN (ISBN-13): 9780387945873
ISBN (ISBN-10): 0387945873
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 1999
Herausgeber: Springer
723 Seiten
Gewicht: 2,066 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 2007-04-27T12:44:11+02:00 (Berlin)
Detailseite zuletzt geändert am 2023-11-28T09:34:23+01:00 (Berlin)
ISBN/EAN: 9780387945873

ISBN - alternative Schreibweisen:
0-387-94587-3, 978-0-387-94587-3
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: ron mittelhammer, fields
Titel des Buches: mathematical statistics for economics and business, eco, business math, mathematica statistics, the business economics, all statistics

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Daten vom Verlag:

Autor/in: Ron C. Mittelhammer
Titel: Mathematical Statistics for Economics and Business
Verlag: Springer; Springer US
724 Seiten
Erscheinungsjahr: 1999-05-27
New York; NY; US
Gewicht: 2,035 kg
Sprache: Englisch
114,44 € (DE)
117,65 € (AT)
166,16 CHF (CH)
Not available, publisher indicates OP

BB; Book; Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Wahrscheinlichkeitsrechnung und Statistik; Verstehen; mathematical statistics; Probability theory; Statistical Models; econometrics; Estimator; Normal distribution; Analysis; Random variable; STATISTICA; A; Probability Theory and Stochastic Processes; Mathematics and Statistics; Econometrics; Applications of Mathematics; Statistics, general; Stochastik; Ökonometrie und Wirtschaftsstatistik; Angewandte Mathematik; Wahrscheinlichkeitsrechnung und Statistik; BC; EA; BB

1. Elements of Probability Theory.- 1.1. Introduction.- 1.2. Experiment, Sample Space, Outcome, and Event.- 1.3. Nonaxiomatic Probability Definitions.- 1.4. Axiomatic Definition of Probability.- 1.5. Some Probability Theorems.- 1.6. A Digression on Events.- 1.7. Conditional Probability.- 1.8. Independence.- 1.9. Bayes’s Rule.- Key Words, Phrases, and Symbols.- Problems.- 2. Random Variables, Densities, and Cumulative Distribution Functions.- 2.1. Introduction.- 2.2. Univariate Random Variables and Density Functions.- Probability Space Induced by a Random Variable.- Discrete Random Variables and Probability Density Functions.- Continuous Random Variables and Probability Density Functions.- Classes of Discrete and Continuous PDFs.- Mixed Discrete-Continuous Random Variables.- 2.3. Univariate Cumulative Distribution Functions.- CDF Properties.- Duality Between CDFs and PDFs.- 2.4. Multivariate Random Variables, PDFs, and CDFs.- Multivariate Random Variable Properties and Classes of PDFs.- Multivariate CDFs and Duality with PDFs.- Multivariate Mixed Discrete-Continuous and Composite Random Variables.- 2.5. Marginal Probability Density Functions and CDFs.- Bivariate Case.- N-Variate Case.- Marginal Cumulative Distribution Functions (MCDFs).- 2.6. Conditional Density Functions.- Bivariate Case.- Conditioning on Elementary Events in Continuous Cases.- N-Variate Case.- Conditional CDFs.- 2.7. Independence of Random Variables.- Bivariate Case.- N-Variate.- Independence Between Random Vectors and Between Functions of Random Vectors.- 2.8. Extended Example of Multivariate Concepts in the Continuous Case.- 2.9. Events Occurring with Probability Zero.- Key Words, Phrases, and Symbols.- Problems.- 3. Mathematical Expectation and Moments.- 3.1. Expectation of a Random Variable.- 3.2. Expectation of a Function of Random Variables.- Expectation Properties.- Multivariate Extensions.- 3.3. Conditional Expectation.- Regression Function.- Conditional Expectation and Regression in the Multivariate Case.- 3.4. Moments of a Random Variable.- Relationship Between Moments About the Origin and Mean.- Existence of Moments.- Nonmoment Measures of Probability Density Characteristics.- 3.5. Moment- and Cumulant-Generating Functions.- Uniqueness and Inversion of MGFs.- Cumulant-Generating Function.- Multivariate Extensions.- 3.6. Joint Moments, Covariance, and Correlation.- Covariance and Correlation.- Correlation, Linear Association, and Degeneracy.- 3.7. Means and Variances of Linear Combinations of Random Variables.- 3.8. Necessary and Sufficient Conditions for Positive Semidefiniteness.- Key Words, Phrases, and Symbols.- Problems.- 4. Parametric Families of Density Functions.- 4.1. Parametric Families of Discrete Density Functions.- Family Name: Uniform.- Family Name: Bernoulli.- Family Name: Binomial.- Family Name: Multinomial.- Family Name: Negative Binomial and Geometric.- Family Name: Poisson.- Family Name: Hypergeometric.- Family Name: Multivariate Hypergeometric.- 4.2. Parametric Families of Continuous Density Functions.- Family Name: Uniform.- Family Name: Gamma.- Gamma Subfamily Name: Exponential.- Gamma Subfamily Name: Chi-Square.- Family Name: Beta.- 4.3. The Normal Family of Densities.- Family Name: Univariate Normal.- Family Name: Multivariate Normal Density.- 4.4. The Exponential Class of Densities.- Key Words, Phrases, and Symbols.- Problems.- 5. Basic Asymptotics.- 5.1. Introduction.- 5.2. Elements of Real Analysis.- Limit of a Sequence.- Continuous Functions.- Convergence of Function Sequence.- Order of Magnitude of a Sequence.- 5.3. Types of Random-Variable Convergence.- Convergence in Distribution.- Convergence in Probability.- Convergence in Mean Square (or Convergence in Quadratic Mean).- * Almost-Sure Convergence (or Convergence with Probability 1).- Relationships Between Convergence Modes.- 5.4. Laws of Large Numbers.- Weak Laws of Large Numbers (WLLN).- *Strong Laws of Large Numbers (SLLN).- 5.5. Central Limit Theorems.- Independent Scalar Random Variables.- *Dependent Random Variables.- Multivariate Central Limit Results.- 5.6. Asymptotic Distributions of Differentiable Functions of Asymptotically Normally Distributed Random Variables.- Key Words, Phrases, and Symbols.- Problems.- 6. Sampling, Sample Moments, Sampling Distributions, and Simulation.- 6.1. Introduction.- 6.2. Random Sampling.- Random Sampling from a Population Distribution.- Random Sampling Without Replacement.- Sample Generated by a Composite Experiment.- Commonalities in Probabilistic Structure of Random Samples.- Statistics.- 6.3. Empirical or Sample Distribution Function.- EDF: Scalar Case.- EDF: Multivariate Case.- 6.4. Sample Moments and Sample Correlation.- Scalar Case.- Multivariate Case.- 6.5. Properties of X-n and S2n When Random Sampling from a Normal Distribution?.- 6.6. Sampling Distributions: Deriving Probability Densities of Functions of Random Variables.- MGF Approach.- CDF Approach.- Equivalent Events Approach (Discrete Case).- Change of Variables (Continuous Case).- 6.7. t-and F-Densities.- t-Density.- Family Name: t-Family.- F-Density.- Family Name: F-Family.- 6.8. Random Sample Simulation and the Probability Integral Transformation.- 6.9. Order Statistics.- Key Words, Phrases, and Symbols.- Problems.- 7. Elements of Point Estimation Theory.- 7.1. Introduction.- 7.2. Statistical Models.- 7.3. Estimators and Estimator Properties.- Estimators.- Estimator Properties.- Finite Sample Properties.- Asymptotic Properties.- Class of Consistent Asymptotically Normal (CAN) Estimators and Asymptotic Properties.- 7.4. Sufficient Statistics.- Minimal Sufficient Statistics.- Sufficient Statistics in the Exponential Class.- Sufficiency and the MSE Criterion.- Complete Sufficient Statistics.- Sufficiency, Minimality, and Completeness of Functions of Sufficient Statistics.- 7.5. Results on MVUE Estimation.- Cramér-Rao Lower Bound.- Complete Sufficient Statistics and MVUEs.- Key Words, Phrases, and Symbols.- Problems.- 8. Point Estimation Methods.- 8.1. Introduction.- 8.2. Least Squares and the General Linear Model.- The Classical GLM Assumptions.- Estimator for ? Under Classical GLM Assumptions.- Estimator for ?2 Under Classical GLM Assumptions.- Consistency of ?^.- Consistency of ?2.- Asymptotic Normality of ?^.- Asymptotic Normality of ?2.- Summary of Estimator Properties.- Violations of Classic GLM Assumptions.- GLM Assumption Violations: Property Summary and Epilogue.- Least Squares Under Normality.- MVUE Property of ?^ and ?2.- 8.3. The Method of Maximum Likelihood.- MLE Mechanics.- MLE Properties: Finite Sample.- MLE Properties: Large Sample.- MLE Invariance Principle.- MLE Property Summary.- 8.4. The Method of Moments.- Method of Moments Estimator.- MOM Estimator Properties.- Generalized Method of Moments (GMM) sEstimator.- GMM Properties.- Key Words, Phrases, and Symbols.- Problems.- 9. Elements of Hypothesis-Testing Theory.- 9.1. Introduction.- 9.2. Statistical Hypotheses.- 9.3. Basic Hypothesis-Testing Concepts.- Statistical Hypothesis Tests.- Type I Error, Type II Error, and Ideal Statistical Tests.- Controlling Type I and II Errors.- Type I/Type II Error Tradeoff.- Test Statistics.- Null and Alternative Hypotheses.- 9.4. Parametric Hypothesis Tests and Test Properties.- Maintained Hypothesis.- Power Function.- Properties of Statistical Tests.- P Values.- Asymptotic Tests.- 9.5. Results on UMP Tests.- Neyman-Pearson Approach.- Monotone Likelihood Ratio Approach.- Exponential Class of Densities.- * Conditioning in the Multiple Parameter Case.- Concluding Remarks.- 9.6. Noncentral t-Distribution.- Family Name: Noncentral t-Distribution.- Key Words, Phrases, and Symbols.- Problems.- 10. Hypothesis-Testing Methods.- 10.1. Introduction.- 10.2. Heuristic Approach.- 10.3. Generalized Likelihood Ratio Tests.- Test Properties: Finite Sample.- Test Properties: Asymptotics.- 10.4. Lagrange Multiplier Tests.- 10.5. Wald Tests.- 10.6. Tests in the GLM.- Tests When ? Is Multivariate Normal.- Testing R? = r, R? ? r, Or R? ? r When R Is (1× k): T-Tests.- Bonferroni Joint Tests of Ri? = ri; Ri? ? ri, or Ri? ? ri, i=1,…, m.- Testing When ? Is Not Multivariate Normal.- Testing R? = r or R(?) = r When R Has q Rows: Asymptotic ?2-Tests.- Testing R(?) = r, R(?) ? r, or R(?) ? r When R Is a Scalar Function: Asymptotic Normal Tests.- 10.7. Confidence Intervals and Regions.- Defining Confidence Regions via Duality with Critical Regions.- Properties of Confidence Regions.- Confidence Regions from Pivotal Quantities.- Confidence Regions as Hypothesis Tests.- 10.8. Nonparametric Tests of Distributional Assumptions.- Functional Forms of Probability Distributions.- IID Assumption.- 10.9. Noncentral ?2 - and P-Distributions.- Family Name: Noncentral ?2-Distribution.- Family Name: Noncentral F-Distribution.- Key Words, Phrases, and Symbols.- Problems.- Appendix A. Math Review: Sets, Functions, Permutations, Combinations, and Notation.- A.1. Introduction.- A.2. Definitions, Axioms, Theorems, Corollaries, and Lemmas.- A.3. Elements of Set Theory.- Set-Defining Methods.- Set Classifications.- Special Sets, Set Operations, and Set Relationships.- Rules Governing Set Operations.- A.4. Relations, Point Functions, and Set Functions.- Cartesian Product.- Relation (Binary).- Function.- Real-Valued Point Versus Set Functions.- A.5. Combinations and Permutations.- A.6. Summation, Integration and Matrix Differentiation Notation.- Key Words, Phrases, and Symbols.- Problems.- Appendix B. Useful Tables.- B.1. Cumulative Normal Distribution.- B.2. Student’s t Distribution.- B.3. Chi-square Distribution.- B.4. F-Distribution: 5% Points.- B.5. F-Distribution: 1% Points.