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AuthorMittelhammer, Ron C. author
TitleMathematical Statistics for Economics and Business [electronic resource] / by Ron C. Mittelhammer
ImprintNew York, NY : Springer New York, 1996
Connect tohttp://dx.doi.org/10.1007/978-1-4612-3988-8
Descript XVIII, 724 p. online resource

SUMMARY

This book is designed to provide beginning graduate stuยญ dents and advanced undergraduates with a rigorous and accessible foundation in the principles of probability and mathematical statistics underlying statisยญ tical inference in the fields of business and economics. The book assumes no prior knowledge of probability or statistics and effectively builds the subject "from the ground up." Students who complete their studies of the topics in this text will have acquired the necessary background to achieve a mature and enduring understanding of statistical and econometric methods of inference and will be well equipped to read and comprehend graduate-level econometยญ rics texts. Additionally, this text serves as an effective bridge to more advanced study of both mathematical statistics and econometric theory and methods. The book will also be of interest to researchers who desire a decidedly business and economics-oriented treatment of the subject in terms of its topics, depth, breadth, examples, and problems


CONTENT

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. Bayesโ{128}{153}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 -- 2.3. Univariate Cumulative Distribution Functions -- 2.4. Multivariate Random Variables, PDFs, and CDFs -- 2.5. Marginal Probability Density Functions and CDFs -- 2.6. Conditional Density Functions -- 2.7. Independence of Random Variables -- 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 -- 3.3. Conditional Expectation -- 3.4. Moments of a Random Variable -- 3.5. Moment- and Cumulant-Generating Functions -- 3.6. Joint Moments, Covariance, and Correlation -- 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 -- 4.2. Parametric Families of Continuous Density Functions -- 4.3. The Normal Family of Densities -- 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 -- 5.3. Types of Random-Variable Convergence -- 5.4. Laws of Large Numbers -- 5.5. Central Limit Theorems -- 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 -- 6.3. Empirical or Sample Distribution Function -- 6.4. Sample Moments and Sample Correlation -- 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 -- 6.7. t-and F-Densities -- 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 -- 7.4. Sufficient Statistics -- 7.5. Results on MVUE Estimation -- Key Words, Phrases, and Symbols -- Problems -- 8. Point Estimation Methods -- 8.1. Introduction -- 8.2. Least Squares and the General Linear Model -- 8.3. The Method of Maximum Likelihood -- 8.4. The Method of Moments -- 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 -- 9.4. Parametric Hypothesis Tests and Test Properties -- 9.5. Results on UMP Tests -- 9.6. 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 -- 10.4. Lagrange Multiplier Tests -- 10.5. Wald Tests -- 10.6. Tests in the GLM -- 10.7. Confidence Intervals and Regions -- 10.8. Nonparametric Tests of Distributional Assumptions -- 10.9. Noncentral ?2 - and P-Distributions -- 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. Studentโ{128}{153}s t Distribution -- B.3. Chi-square Distribution -- B.4. F-Distribution: 5% Points -- B.5. F-Distribution: 1% Points


Mathematics Applied mathematics Engineering mathematics Probabilities Statistics Econometrics Mathematics Probability Theory and Stochastic Processes Econometrics Applications of Mathematics Statistics general



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