Community articles — Math

A lecture on intermediate proofs that I taught at ARML.

Linear regression is one of the most widely used statistical methods available today. It is used by data analysts and students in almost every discipline. However, for the standard ordinary least squares method, there are several strong assumptions made about data that is often not true in real world data sets. This can cause numerous problems in the least squares model. One of the most common issues is a model overfitting the data. Ridge Regression and LASSO are two methods used to create a better and more accurate model. I will discuss how overfitting arises in least squares models and the reasoning for using Ridge Regression and LASSO include analysis of real world example data and compare these methods with OLS and each other to further infer the benefits and drawbacks of each method.

Under a partly linear model we study a family of robust estimates for the regression parameter and the regression function when some of the predictors take values on a Riemannian manifold. We obtain the consistency and the asymptotic normality of the proposed estimators. Simulations and an application to a real dataset show the good performance of our proposal under small samples and contamination.

Lecturas tomadas de la clase de M.Sc. Fidel Ordoñez, Carrera de Matemática UNAH, 2014

TTIC 31020 : Problem Set 1

Teoría de números

A rigorous construction of the field of real numbers: the unique (up to isomorphism) completely ordered field with the least upper bound property; along with various formulations of completeness and with a postlude on the measure of sets.

We describe what mimetic interpolation is and why it is critical for some pre- and post-processing tasks. A simple test case shows how using bilinear interpolation for a flux calculation introduces numerical errors that depend on the grid, the number of segments and the number of quadrature points. In contrast, mimetic interpolation will return the exact result regardless of the grid resolution and the number of segments.

Can there be a polynomial with infinite solutions? If so, would it be a polynomial? Also, would it have an infinite solution set? Let's find out.