Statistical Computing & Optimization Methods (MTH210)

This repository contains the code and report for my MTH210 Statistical Computing project.

Project Overview

The project focuses on estimating complex distribution parameters using robust mathematical optimization and statistical resampling techniques.

Key Features & Methodologies

• Maximum Likelihood Estimation (MLE): Implemented using the Newton-Raphson algorithm to optimize log-likelihood surfaces.
• Confidence Intervals: Constructed 95% CIs using both Parametric and Non-Parametric Bootstrap methods (1,000 replications).
• Additional Optimization Techniques: Integrated the Bisection Method for root-finding and the Expectation-Maximization (EM) algorithm.
• Algorithmic Convergence: Ensured strict convergence criteria ($< 10^{-6}$) and evaluated Hessian matrices for accurate results.

Files

• MTH 210 Project Code.R: The complete R script containing the implementation of the algorithms.
• MTH 210 Project Report.pdf: Detailed mathematical formulations, iteration tables, and statistical inference results.