Cornerstones in Quantitative Empirical Methods - Volume I: Foundations provides a complete, self-contained path from first principles to modern statistical inference, giving a comprehensive technical foundation for understanding and analyzing data problems using quantitative methods. The first part of the book provides a thorough introduction to probability theory and statistics with a focus on techniques and concepts, which are particularly useful for empirical analyses. Building directly on the first part, the second part of the book provides an introduction to estimation theory, hypothesis testing, likelihood theory, and Bayesian methods.
The nineteen concise chapters follow a transparent pattern: motivation and intuition, carefully chosen examples, main results stated as formal theorems, and a curated set of exercises that reinforce both computation and reasoning. Short illustrative datasets keep the exposition concrete while maintaining the book’s primary focus on theory. Three appendices consolidate the required background in set theory, real analysis, and simulation techniques, making the volume fully self-contained.
Designed for graduate and advanced-undergraduate courses in e.g. economics, political science, business analytics, or data science—or for motivated self-study—Volume I equips readers with the concepts and techniques needed for quantitative empirical analysis. It also prepares readers for Volume II, which builds the foundation for modelling, prediction, and causal inference in empirical studies.
Key Features:
- Comprehensive coverage across the technical fields of probability theory, statistics, and mathematics, needed to understand and perform in-depth empirical modelling and analysis
- Extensive treatment of estimation theory and various estimation methods, such as analog estimators, maximum likelihood estimators and Bayesian methods
- Elaborate discussion of hypothesis testing and recommendations to avoid pitfalls
- Inclusion of technical details and proofs structured such that they can be skipped by readers who prefer a less technical, though still cohesive, approach
Table of Contents:
1 Basic elements in probability theory 2 Distribution of a random variable 3 Joint distribution of random variables 4 Conditional distribution of a random variable 5 Aspects of a univariate distribution 6 Aspects of a multivariate distribution 7 Independence between random variables 8 Commonly used univariate distributions 9 Bivariate normal distributions 10 Distribution of a sample 11 Estimation theory 12 Estimating aspects of a univariate distribution 13 Estimation of a sampling distribution 14 Confidence intervals 15 Analysis of hypotheses 16 Test of hypotheses 17 Maximum likelihood estimation 18 Inference with maximum likelihood estimation 19 Bayesian methods 20 Appendix A: Probability theory 21 Appendix B: Real analysis 22 Appendix C: Simulation from a distribution
About the Author :
Mikkel Bennedsen, PhD, is Associate Professor at the Department of Economics and Business Economics, Aarhus University. He has received several teaching honors, including the university’s Best Lecturer award (2024). His research spans theoretical and applied econometrics, stochastic processes, and energy economics.
Allan H. Würtz, PhD, is Associate Professor and Head of the Econometrics and Business Analytics section at the Department of Economics and Business Economics, Aarhus University. An award-winning instructor, he is the author of the introductory text An Insight into Statistics and has published on econometric methodology.
