Statistics for Economists and Intelligent Data Analysts
Designed by Professor Sasha Shapoval
University of Lodz
Introduction¶
This is a “practical” course that covers a few selected concepts and tools that are most needed
for working with models in Economics and Finance. Although readers may be familiar with
the introductory concepts from the course, we will soon jump into topics that do not get enough
attention in the curriculum of any undergraduate math programs, including the best ones.
In this course, we will rarely discuss proofs. The presentation of the methods and results is focused on their implementations. Therefore, all required codes are attached and discussed. The purpose is to help readers think like economists and get the experience of computer scientists. The readers will train their intuition and enlarge a practical toolkit that solves actual statistical problems. Eventually, this will lead us to important insights about the world around us.
In this course, we will rarely discuss proofs. The presentation of the methods and results is focused on their implementations. Therefore, all required codes are attached and discussed. The purpose is to help readers think like economists and get the experience of computer scientists. The readers will train their intuition and enlarge a practical toolkit that solves actual statistical problems. Eventually, this will lead us to important insights about the world around us.
Topics:
Bayesian approach. Example: spam filter
Basic knowledge of probabilities. Random variables, probability distribution function, cumulative distribution functions. Transformation of random variables. Exponential distribution. The sum of independent random variables. Convolution. The sum of exponential distributions and the gamma distribution. Waiting time paradox. Persistence of bad luck. Ratios. Order statistics and Cauchy distribution. Empirical distributions. Kolmogorov-Smirnov statistics. Independence on the true distribution
Statistical tests. Hypotheses, test statistics, significance level, power. Linear test statistics, the Fisher discriminant function. Nonlinear test statistics, neural networks. Goodness-of-fit tests. Pearson chi-square test
Inverse cumulative distribution function. Bootstrap
General concepts of parameter estimation. Point estimators. Estimators for mean, variance, covariance. Bias. Method of moments. The method of maximum likelihood. Maximum likelihood with binned data. Relationship between ML and Bayesian estimators. The method of least squares. Connection with maximum likelihood Testing goodness-of-fit with chi-squared. Statistical errors and confidence intervals
Regressions. Unbiasedness of the regression coefficients. The variance and the confidence interval of the slope of the response variable. Hypothesis: the slope is zero.
Literature:
Bruce E. Hansen, Probability and Statistics for Economists
Larry Wasserman, All of Nonparametric Statistics
Glen Cowan, Statistical Data Analysis
Jeffrey M. Wooldridge, Introductory Econometrics: A Modern Approach
William Feller, An Introduction to Probability Theory and Its Applications
John S. Conery. Explorations in Computing: An Introduction to Computer Science and Python Programming (elementary introduction to Python)
Allen B. Downey Think Stats: Probability and Statistics for Programmers (the handbook can be considered as elementary practical introduction to various topics of our discipline)
Next: Review of probabilities
Distributed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) license