Codes and examples of discussion sessions for course GRS MA 681 at Boston University, Fall 2019.
Sept. 16. Central Limit Theorem (CLT) for iid observations and not iid observations, Delta Method
Sept. 23. Histograms, density estimation using Kernel methods, KS-plots, QQ-plots, Empirical CDF, an example of Bootstrap (Temperature data was used this session)
Sept. 29. Maximum Likelihood Estimation (MLE), Method of Moments (MoM), bias and variance of estimators, Mean Squared Errors (MSE), Bias-Variance tradeoff
Oct. 7. Hypothesis Testing (one sided and two sided), Wald Tests with and without Bootstrap, Likelihood Ratio Tests, Fisher Information, p-value, type-1 and type-2 errors, An example of all of these with Poisson data
Oct. 15. Muti-variate Hypothesis Testing, Multiplicity in Hypothesis Testing, Bonferroni method, Benjamin-Hochberg method, type-1 error and type-2 error
Oct. 21. Linear models, Fisher Information Covariance matrix, Wald-Test and MLRT for linear models, t-student test, F-test
Oct. 28 Extended linear models, factors and discrete random variables in linear models, Polynomial linear models, AIC, BIC, cross-validation methods, Forward and Backward stepwise linear regression
Nov. 4 Generalized Linear Models (GLM), Logistic regression, extended logistic regression, classifying with linear and quadratic boundaries
Nov. 11 The general outline for GLMs, Gamma GLM, Comparison between Gamma and Normal GLM (constant and non-constant variablity bands), Polynomial regression to approximate any continous functions
Nov. 18 Time series, AR models, MA models, ARMA models, ARMAX models and their relation to linear regression. Using AIC/BIC, autocorrelation function (acf) and partial autocorrelation function (pacf) in choosing tuning parameters for ARMAX model.
Nov. 25 Fourier representation of time series, Finding Fourier coefficients, Spectral Analysis, Harmonic regression and its relation with linear regression, Confidence intervals and hypothesis testing for harmonic regresison, Observing that just sine and cosine functions are not enough!
Dec. 2 Advantages/disadvantages of Neural Networks, Logistic Regression, Tree-based methods, k-nearest neighborhood methods, and SVM and implementing them on a well-known classifying problem
Dec. 9 Bayesian Approach, an exmaple where the likelihood approach fails and how the Bayesian approach can fix the problem, a quick review of K-means.