RATE OF CONVERGENCE OF MAXIMUM LIKELIHOOD ESTIMATORS UNDER RELAXED SMOOTHNESS CONDITIONS ON THE LIKELIHOOD FUNCTION

This report reviews literature on the rate of convergence of maximum likelihood estimators and establishes a Central Limit Theorem, which yields an O(1/sqrt(n)) rate of convergence of the maximum likelihood estimator under somewhat relaxed smoothness conditions. These conditions include the existence of a one-sided derivative in θ of the pdf, compared to up to three that are classically required. A verification through simulation is included in the end of the report.

EFFECTIVE FUNCTION CHOICE IN THE R SCRIPTING LANGUAGE

This project examines the current available work on the explicit and implicit parallelization of the R scripting language and reports on experimental findings for the development of a model for predicting effective points for automatic parallelization to be performed, based upon input data sizes and function complexity. After finding or creating a series of custom benchmarks, an interval based on data size and time complexity where replacement becomes a viable option was found; specifically between O(N) and O(N3) exclusive. As data size increases, the benefits of parallel processing become more apparent and a point is reached where those benefits outweigh the costs in memory transfer time. Based on our observations, this point can be predicted with a fair amount of accuracy using regression on a sample of approximately ten data sizes spread evenly between a system determined minimum and maximum size.