TY  - BOOK
AU  - Hansen,Bruce E.
TI  - Probability and statistics for economists
SN  - 0691235945
AV  - HB139 .H3638 2022
U1  - 330.015195 23
PY  - 2022///]
CY  - Princeton
PB  - Princeton University Press
KW  - Econometrics
KW  - Probabilities
KW  - Statistics
KW  - Probability
N1  - Includes bibliographical references and index; 1; Basic Probability Theory --; 1.1; Introduction --; 1.2; Outcomes and Events --; 1.3; Probability Function --; 1.4; Properties of the Probability Function --; 1.5; Equally Likely Outcomes --; 1.6; Joint Events --; 1.7; Conditional Probability --; 1.8; Independence --; 1.9; Law of Total Probability --; 1.10; Bayes Rule --; 1.11; Permutations and Combinations --; 1.12; Sampling with and without Replacement --; 1.13; Poker Hands --; 1.14; Sigma Fields* --; 1.15; Technical Proofs* --; 1.16; Exercises -- --; 2; Random Variables --; 2.1; Introduction --; 2.2; Random Variables --; 2.3; Discrete Random Variables --; 2.4; Transformations --; 2.5; Expectation --; 2.6; Finiteness of Expectations --; 2.7; Distribution Function --; 2.8; Continuous Random Variables --; 2.9; Quantiles --; 2.10; Density Functions --; 2.11; Transformations of Continuous Random Variables --; 2.12; Non-Monotonic Transformations --; 2.13; Expectation of Continuous Random Variables --; 2.14; Finiteness of Expectations --; 2.15; Unifying Notation --; 2.16; Mean and Variance --; 2.17; Moments --; 2.18; Jensen's Inequality --; 2.19; Applications of Jensen's Inequality* --; 2.20; Symmetric Distributions --; 2.21; Truncated Distributions --; 2.22; Censored Distributions --; 2.23; Moment Generating Function --; 2.24; Cumulants --; 2.25; Characteristic Function --; 2.26; Expectation: Mathematical Details* --; 2.27; Exercises -- --; 3; Parametric Distributions --; 3.1; Introduction --; 3.2; Bernoulli Distribution --; 3.3; Rademacher Distribution --; 3.4; Binomial Distribution --; 3.5; Multinomial Distribution --; 3.6; Poisson Distribution --; 3.7; Negative Binomial Distribution --; 3.8; Uniform Distribution --; 3.9; Exponential Distribution --; 3.10; Double Exponential Distribution --; 3.11; Generalized Exponential Distribution --; 3.12; Normal Distribution --; 3.13; Cauchy Distribution --; 3.14; Student t Distribution --; 3.15; Logistic Distribution --; 3.16; Chi-Square Distribution --; 3.17; Gamma Distribution --; 3.18; F Distribution --; 3.19; Non-Central Chi-Square --; 3.20; Beta Distribution --; 3.21; Pareto Distribution --; 3.22; Lognormal Distribution --; 3.23; Weibull Distribution --; 3.24; Extreme Value Distribution --; 3.25; Mixtures of Normals --; 3.26; Technical Proofs* --; 3.27; Exercises -- --; 4; Multivariate Distributions --; 4.1; Introduction --; 4.2; Bivariate Random Variables --; 4.3; Bivariate Distribution Functions --; 4.4; Probability Mass Function --; 4.5; Probability Density Function --; 4.6; Marginal Distribution --; 4.7; Bivariate Expectation --; 4.8; Conditional Distribution for Discrete X --; 4.9; Conditional Distribution for Continuous X --; 4.10; Visualizing Conditional Densities --; 4.11; Independence --; 4.12; Covariance and Correlation --; 4.13; Cauchy-Schwarz Inequality --; 4.14; Conditional Expectation --; 4.15; Law of Iterated Expectations --; 4.16; Conditional Variance --; 4.17; H ölder's and Minkowski's Inequalities* --; 4.18; Vector Notation --; 4.19; Triangle Inequalities* --; 4.20; Multivariate Random Vectors --; 4.21; Pairs of Multivariate Vectors --; 4.22; Multivariate Transformations --; 4.23; Convolutions --; 4.24; Hierarchical Distributions --; 4.25; Existence and Uniqueness of the Conditional Expectation* --; 4.26; Identification --; 4.27; Exercises -- --; 5; Normal and Related Distributions --; 5.1; Introduction --; 5.2; Univariate Normal --; 5.3; Moments of the Normal Distribution --; 5.4; Normal Cumulants --; 5.5; Normal Quantiles --; 5.6; Truncated and Censored Normal Distributions --; 5.7; Multivariate Normal --; 5.8; Properties of the Multivariate Normal --; 5.9; Chi-Square, t,F , and Cauchy Distributions --; 5.10; Hermite Polynomials* --; 5.11; Technical Proofs* --; 5.12; Exercises -- --; 6; Sampling --; 6.1; Introduction --; 6.2; Samples --; 6.3; Empirical Illustration --; 6.4; Statistics, Parameters, and Estimators --; 6.5; Sample Mean --; 6.6; Expected Value of Transformations --; 6.7; Functions of Parameters --; 6.8; Sampling Distribution --; 6.9; Estimation Bias --; 6.10; Estimation Variance --; 6.11; Mean Squared Error --; 6.12; Best Unbiased Estimator --; 6.13; Estimation of Variance --; 6.14; Standard Error --; 6.15; Multivariate Means --; 6.16; Order Statistics∗ --; 6.17; Higher Moments of Sample Mean* --; 6.18; Normal Sampling Model --; 6.19; Normal Residuals --; 6.20; Normal Variance Estimation --; 6.21; Studentized Ratio --; 6.22; Multivariate Normal Sampling --; 6.23; Exercises -- --; 7; Law of Large Numbers --; 7.1; Introduction --; 7.2; Asymptotic Limits --; 7.3; Convergence in Probability --; 7.4; Chebyshev's Inequality --; 7.5; Weak Law of Large Numbers --; 7.6; Counterexamples --; 7.7; Examples --; 7.8; Illustrating Chebyshev's Inequality --; 7.9; Vector-Valued Moments --; 7.10; Continuous Mapping Theorem --; 7.11; Examples --; 7.12; Uniformity Over Distributions* --; 7.13; Almost Sure Convergence and the Strong Law* --; 7.14; Technical Proofs* --; 7.15; Exercises -- --; 8; Central Limit Theory --; 8.1; Introduction --; 8.2; Convergence in Distribution --; 8.3; Sample Mean --; 8.4; A Moment Investigation --; 8.5; Convergence of the Moment Generating Function --; 8.6; Central Limit Theorem --; 8.7; Applying the Central Limit Theorem --; 8.8; Multivariate Central Limit Theorem --; 8.9; Delta Method --; 8.10; Examples --; 8.11; Asymptotic Distribution for Plug-In Estimator --; 8.12; Covariance Matrix Estimation --; 8.13; t -Ratios --; 8.14; Stochastic Order Symbols --; 8.15; Technical Proofs* --; 8.16; Exercises -- --; 9; Advanced Asymptotic Theory* --; 9.1; Introduction --; 9.2; Heterogeneous Central Limit Theory --; 9.3; Multivariate Heterogeneous Central Limit Theory --; 9.4; Uniform Central Limit Theory --; 9.5; Uniform Integrability --; 9.6; Uniform Stochastic Bounds --; 9.7; Convergence of Moments --; 9.8; Edgeworth Expansion for the Sample Mean --; 9.9; Edgeworth Expansion for Smooth Function Model --; 9.10; Cornish-Fisher Expansions --; 9.11; Technical Proofs* -- --; 10; Maximum Likelihood Estimation --; 10.1; Introduction --; 10.2; Parametric Model --; 10.3; Likelihood --; 10.4; Likelihood Analog Principle --; 10.5; Invariance Property --; 10.6; Examples --; 10.7; Score, Hessian, and Information --; 10.8; Examples --; 10.9; Cram ér-Rao Lower Bound --; 10.10; Examples --; 10.11; Cram ér-Rao Bound for Functions of Parameters --; 10.12; Consistent Estimation --; 10.13; Asymptotic Normality --; 10.14; Asymptotic Cram ér-Rao Efficiency --; 10.15; Variance Estimation --; 10.16; Kullback-Leibler Divergence --; 10.17; Approximating Models --; 10.18; Distribution of the MLE under Misspecification --; 10.19; Variance Estimation under Misspecification --; 10.20; Technical Proofs* --; 10.21; Exercises -- --; 11; Method of Moments --; 11.1; Introduction --; 11.2; Multivariate Means --; 11.3; Moments --; 11.4; Smooth Functions --; 11.5; Central Moments --; 11.6; Best Unbiased Estimation --; 11.7; Parametric Models --; 11.8; Examples of Parametric Models --; 11.9; Moment Equations --; 11.10; Asymptotic Distribution for Moment Equations --; 11.11; Example: Euler Equation --; 11.12; Empirical Distribution Function --; 11.13; Sample Quantiles --; 11.14; Robust Variance Estimation --; 11.15; Technical Proofs* --; 11.16; Exercises -- --; 12; Numerical Optimization --; 12.1; Introduction --; 12.2; Numerical Function Evaluation and Differentiation --; 12.3; Root Finding --; 12.4; Minimization in One Dimension --; 12.5; Failures of Minimization --; 12.6; Minimization in Multiple Dimensions --; 12.7; Constrained Optimization --; 12.8; Nested Minimization --; 12.9; Tips and Tricks --; 12.10; Exercises -- --; 13; Hypothesis Testing --; 13.1; Introduction --; 13.2; Hypotheses --; 13.3; Acceptance and Rejection --; 13.4; Type I and Type II Errors --; 13.5; One-Sided Tests --; 13.6; Two-Sided Tests --; 13.7; What Does "Accept ℍ0" Mean about ℍ0? --; 13.8; t Test with Normal Sampling --; 13.9; Asymptotic t Test --; 13.10; Likelihood Ratio Test for Simple Hypotheses --; 13.11; Neyman-Pearson Lemma --; 13.12; Likelihood Ratio Test against Composite Alternatives --; 13.13; Likelihood Ratio and t Tests --; 13.14; Statistical Significance --; 13.15; p-Value --; 13.16; Composite Null Hypothesis --; 13.17; Asymptotic Uniformity --; 13.18; Summary --; 13.19; Exercises -- --; 14; Confidence Intervals --; 14.1; Introduction --; 14.2; Definitions --; 14.3; Simple Confidence Intervals --; 14.4; Confidence Intervals for the Sample Mean under Normal Sampling --; 14.5; Confidence Intervals for the Sample Mean under Non-Normal Sampling --; 14.6; Confidence Intervals for Estimated Parameters --; 14.7; Confidence Interval for the Variance --; 14.8; Confidence Intervals by Test Inversion --; 14.9; Use of Confidence Intervals --; 14.10; Uniform Confidence Intervals --; 14.11; Exercises -- --; 15; Shrinkage Estimation --; 15.1; Introduction --; 15.2; Mean Squared Error --; 15.3; Shrinkage --; 15.4; James-Stein Shrinkage Estimator --; 15.5; Numerical Calculation --; 15.6; Interpretation of the Stein Effect --; 15.7; Positive-Part Estimator --; 15.8; Summary --; 15.9; Technical Proofs* --; 15.10; Exercises -- --; 16; Bayesian Methods --; 16.1; Introduction --; 16.2; Bayesian Probability Model --; 16.3; Posterior Density --; 16.4; Bayesian Estimation --; 16.5; Parametric Priors --; 16.6; Normal-Gamma Distribution --; 16.7; Conjugate Prior --; 16.8; Bernoulli Sampling --; 16.9; Normal Sampling --; 16.10; Credible Sets --; 16.11; Bayesian Hypothesis Testing --; 16.12; Sampling Properties in the Normal Model --; 16.13; Asymptotic Distribution --; 16.14; Technical Proofs* --; 16.15; Exercises -- --; 17; Nonparametric Density Estimation --; 17.1; Introduction --; 17.2; Histogram Density Estimation --; 17.3; Kernel Density Estimator --; 17.4; Bias of Density Estimator --; 17.5; Variance of Density Estimator --; 17.6; Variance Estimation and Standard Errors --; 17.7; Integrated Mean Squared Error of Density Estimator --; 17.8; Optimal Kernel --; 17.9; Reference Bandwidth --; 17.10; Sheather-Jones Bandwidth* --; 17.11; Recommendations for Bandwidth Selection --; 17.12; Practical Issues in Density Estimation --; 17.13; Computation --; 17.14; Asymptotic Distribution --; 17.15; Undersmoothing --; 17.16; Technical Proofs* --; 17.17; Exercises -- --; 18; Empirical Process Theory --; 18.1; Introduction --; 18.2; Framework --; 18.3; Glivenko-Cantelli Theorem --; 18.4; Packing, Covering, and Bracketing Numbers --; 18.5; Uniform Law of Large Numbers --; 18.6; Functional Central Limit Theory --; 18.7; Conditions for Asymptotic Equicontinuity --; 18.8; Donsker's Theorem --; 18.9; Technical Proofs* --; 18.10; Exercises -- --; Appendix 1; Limits --; Appendix 2; Series --; Appendix 3; Factorials --; Appendix 4; Exponentials --; Appendix 5; Logarithms --; Appendix 6; Differentiation --; Appendix 7; Mean Value Theorem --; Appendix 8; Integration --; Appendix 9; Gaussian Integral --; Appendix 10; Gamma Function --; Appendix 11; Matrix Algebra
N2  - "A comprehensive introduction to probability and statistics through the perspective of applying it to economic analysis"--
ER  -