Estimación funcional: valor esperado condicional

What is functional estimation for conditional expected value?

Functional estimation of conditional expected value is an essential tool in data analysis. The conditional expected value is interpreted as a function of the independent variable, which can be either linear or nonlinear. Moreover, when the independent variable is categorical, it will present different expected values for different categories. This methodology is not a recent invention; its development rests on deeply rooted mathematical foundations, from Tuki's analysis to Fisher's classical statistics, and even the axioms of probability formulated by Kolmogorov.

What are the typical models for estimating conditional expected value?

There are several commonly used models for the estimation of the conditional expected value, among which the following stand out:

• Linear regression: parametric model with a specific formula defined by its parameters.
• Logistic regression: Another similar parametric model, but suitable for classification problems.
• K-nearest neighbors (KNN): Non-parametric model, which uses training data for prediction.
• Support Vector Machines (SVM): Also a non-parametric model that seeks to find the hyperplane that best separates the different classes.

What is the difference between parametric and non-parametric models?

• Parametric models: Like linear and logistic regression, these models rely on specific formulas with defined parameters. The coefficients of these parameters are calibrated using established statistical and mathematical methods.

• Non-parametric models: In contrast, support vector and K-nearest neighbor machines do not conform to a rigid formula. These techniques cover a broader spectrum of variability in the data, providing estimates through algorithms that attempt to model the complexities of the dependent variable.

How do other models such as neural networks relate?

It is worth noting that although neural networks are categorized as parametric models due to their structure based on trainable parameters, the magnitude of these parameters is such that, in practice, these models often behave as if they were nonparametric. This feature allows neural networks to capture highly complex patterns in the data, but they also present particular challenges in aspects such as interpretability.

What role do these models play in contemporary data science?

Data science, far from being a mere fad, represents the logical evolution of a century of mathematical and statistical work. The implementation of these models provides the necessary tools to understand and predict behaviors in different fields of knowledge.

Becoming interested in data science and its application with these models can open up a world of opportunities. This knowledge not only enriches your skills, but also puts you in a privileged position to face complex analytical challenges. As the experts would say: Don't stop there! Continue to explore and delve deeper into this fascinating world of functional estimation and statistical inference.