Statistical Theory
Explore advanced statistical theory concepts through a comprehensive 5-hour video series. Delve into topics such as sum of squared normal variables, best predictors using functions, alternative expected value formulas, and incomplete beta functions. Learn about confidence intervals for population medians, discrete order statistics, and Poisson probabilities. Discover proofs for the median minimizing absolute loss, Markov and Chebyshev inequalities, and the weak law of large numbers. Study the binomial theorem, big O notation, and correction methods like Holm-Bonferroni and Simes. Examine matrix properties, gamma function characteristics, and distribution approximations. Investigate confidence intervals for population means, moments of sample means, and noncentral chi-square distributions. Gain practical skills using R for bivariate normal probability calculations and generating double exponential data. Explore statistical concepts such as rotational invariance, Kruskal's proof, and deriving cumulative distribution functions for inverse gamma distributions. Read more