DAMSL-102 Mathematical and Computational Statistics

Core

DAMSL-102

B semester

10

Introduction to R
Introduction to Resampling Methods: Cross-Validation
Simulation of Random Variables Monte Carlo Experiments
Bootstrapping Permutation Tests
Simulation of Random Variables
Numerical Solution of Least Squares Problems Iterative Procedures for Model Building
Multimodel Inference
High-Dimensional Data; Regression in High Dimensions Lasso-Type Estimators
Numerical Solution of Maximum Likelihood Equations
Newton-Raphson Algorithm
Generalized Linear Models; The Fisher Scoring Algorithm

Upon successful completion of this course students will have a very good knowledge of R
software.
Furthermore, students will be able to: simulate random numbers from a wide variety of
probability distributions; construct confidence intervals using bootstrap; perform hypothesis
testing via permutations; conduct Monte Carlo experiments to evaluate alternative estimators;
evaluate predictive models using cross-validation.
Upon successful completion of this course students will have understood the algorithms for the
numerical solution of least squares problems and will be able to create their own functions for
stepwise model building.
Upon successful completion of this course students will have learned algorithms for penalized
estimation of least squares and least absolute deviations problems and will be able to evaluate
lasso-type estimators via Monte Carlo experiments.
Upon successful completion of this course students will be able to solve numerically maximum likelihood problems using the Newton-Raphson and Fisher-Scoring Algorithms.