Distributions, estimation, hypothesis testing, regression, and signal detection for quantitative finance.
The bell curve, z-scores, the 68-95-99.7 rule, and the law of large numbers
Uniform, exponential, and log-normal — and when to use each
Why the normal distribution is everywhere
Gamma, chi-squared, Beta distributions, and Bayesian conjugate priors
Point estimation, bias-variance tradeoff, and risk-adjusted returns
p-values, t-tests, Type I/II errors, and statistical significance
Measuring relationships between assets, beta, and diversification
Fitting distributions and estimating parameters from data
Constructing and interpreting intervals for means and proportions
OLS, factor models, residual analysis, and R-squared
Entropy, KL divergence, mutual information, and applications to quant finance
Sign test, Wilcoxon/Mann-Whitney, Kolmogorov-Smirnov, Spearman, and permutation tests
Joint PDFs, bivariate normal, conditional distributions, and Cholesky simulation
Conjugate priors, posterior updating, credible intervals, and Bayes factors
Multicollinearity, heteroscedasticity, Ridge/Lasso, and cross-validation
Stationarity, AR/MA models, ARIMA, and Box-Jenkins methodology
Family-wise error, Bonferroni/Holm, FDR, data snooping, and the deflated Sharpe ratio
Statistical power, effect size, sample-size formulas, and the peeking problem
Eigendecomposition, factor extraction, yield curve PCA, and covariance denoising
Crossover strategies and trend detection
Volatility clustering, GARCH(1,1), and conditional variance forecasting
Non-parametric and parametric bootstrap, percentile/BCa intervals, and block bootstrap for time series
Sklar's theorem, Gaussian and t copulas, GPD/peaks-over-threshold, and the Hill estimator