Lectures related to Quantitative Risk Management: VaR Estimation and Multivariate Distributions

Interval Estimation

Covers the construction of confidence intervals for a normal distribution with unknown mean and variance.

VaR Model Evaluation

Discusses Monte Carlo VaR accuracy, confidence intervals, backtesting, and multivariate distributions.

Estimators and Confidence Intervals

Explores bias, variance, unbiased estimators, and confidence intervals in statistical estimation.

Estimation and Confidence Intervals

Explores bias, variance, and confidence intervals in parameter estimation using examples and distributions.

Statistical Inference: Approximate Critical Values and Confidence Intervals

Covers the construction of confidence intervals and approximate critical values in statistical inference.

Confidence Intervals: Student, Asymptotic Wald

Covers confidence intervals for Gaussian means, Student distribution, and Wald confidence intervals for maximum likelihood estimators.

Confidence Intervals and Hypothesis Testing

Explores confidence intervals, hypothesis testing, and decision-making using test statistics and p-values.

Describing Data: Statistics and Hypothesis Testing

Covers descriptive statistics, hypothesis testing, and correlation analysis with various probability distributions and robust statistics.

Estimation Methods in Probability and Statistics

Discusses estimation methods in probability and statistics, focusing on maximum likelihood estimation and confidence intervals.

Confidence Intervals and MLE Limit Theorems

Explores constructing confidence intervals and MLE limit theorems for large samples.

Statistical Inference: Confidence Intervals

Covers the construction of approximate confidence intervals using the central limit theorem for large sample sizes.

Statistics: Hypothesis Testing & Confidence Intervals

Covers hypothesis testing, confidence intervals, data distributions, and statistical significance in data analysis.

Estimating Parameters: Confidence Intervals

Explores estimating parameters through confidence intervals in linear regression and statistics.

Interval Estimation: Method of Moments

Covers the method of moments for estimating parameters and constructing confidence intervals based on empirical moments matching distribution moments.

Probabilities and Statistics

Covers fundamental concepts in probabilities and statistics, including linear regression, exploratory statistics, and the analysis of probabilities.

Optimality in Statistical Inference

Delves into the duality between confidence intervals and hypothesis tests, emphasizing the importance of precision and accuracy in estimation.

Statistical Theory: Inference and Optimality

Explores constructing confidence regions, inverting hypothesis tests, and the pivotal method, emphasizing the importance of likelihood methods in statistical inference.

Numerical Simulation of SDEs: Monte Carlo & Optimal Control

Covers Monte Carlo methods, variance reduction, and stochastic optimal control, exploring simulation techniques, efficiency, and investment dynamics.

Descriptive Statistics: Hypothesis Testing

Introduces descriptive statistics, hypothesis testing, p-values, and confidence intervals, emphasizing their importance in data analysis.

Risk Measures: Accuracy and Multivariate Distributions

Discusses risk measure evaluation, confidence intervals, and multivariate distributions for portfolio risk assessment.