Mathematics for Data Science Probability Statistical Inference Programming in R Multivariate Analysis Regression Models Advanced Programming

The main course objectives are: 1. Understand the principles of stochastic convergence and notation (OP and oP). 2. Explore the reasons and advantages of using nonparametric statistics. 3. Learn the theory and application of Kernel Density Estimation (KDE) methods, including: - Histograms - Kernel density estimation - Asymptotic properties of KDE - Bandwidth selection for KDE - Address practical issues related to KDE 4. Extend KDE techniques to multivariate data, analyze their asymptotic properties, and apply them to real-world problems. 5. Implement Kernel Regression Estimation (KRE) methods, including: - Kernel regression estimation - Asymptotic properties of KRE - Bandwidth selection for KRE - Explore specialized KRE techniques like Regressogram - Apply KRE to mixed multivariate data 6. Gain proficiency in prediction, confidence interval estimation, and local likelihood using Kernel Regression.78. Understand and perform nonparametric tests, including: - Goodness-of-fit tests for distributions - Comparison of distributions - Independence tests - Other relevant nonparametric tests. These objectives collectively aim to provide a comprehensive understanding of nonparametric statistical methods, their applications, and their theoretical underpinnings.

This course is designed to give a panoramic view of several tools available for nonparametric statistics, at an intermediate-advanced level. This view covers in-depth the main concepts in the estimation of the density and regression functions through kernel methods (with their corresponding applications), and the description of several popular nonparametric tests. The focus is placed on providing the main insights on the statistical/mathematical foundations of the methods and on showing the effective implementation of the methods through the use of statistical software. This is achieved by a mixture of theory and reproducible code. 1. Introduction   1.1. Probability review   1.2. Facts about distributions   1.3. Stochastic convergence review   1.4. OP and oP notation   1.5. Review on basic analytical tools   1.6. Why nonparametric statistics? 2. Kernel density estimation I   2.1. Histograms   2.2. Kernel density estimation   2.3. Asymptotic properties   2.4. Bandwidth selection   2.5. Practical issues   2.6. Kernel density estimation with ks 3. Kernel density estimation II   3.1. Multivariate kernel density estimation   3.2. Asymptotic properties   3.3. Bandwidth selection   3.4. Applications of kernel density estimation 4. Kernel regression estimation I   4.1. Kernel regression estimation   4.2. Asymptotic properties   4.3. Bandwidth selection   4.4. Regressogram   4.5. Kernel regression estimation with np 5. Kernel regression estimation II   5.1. Kernel regression with mixed multivariate data   5.2. Bandwidth selection   5.3. Prediction and confidence intervals   5.4. Local likelihood 6. Nonparametric tests   6.1. Goodness-of-fit tests for distributions   6.2. Comparison of distributions   6.3. Independence tests   6.4. Other tests The program is subject to modifications due to the course development and/or academic calendar.

The lessons consist of a mixture of theory (methods description) and practice (implementation and practical usage of methods). The implementation of the methods is done with the statistical language R. Students are expected to bring their own laptops to experience the code during some parts of the lessons. * Training activities   - AF1: Theoretical lesson.   - AF2: Practical lesson.   - AF5: Tutorials.   - AF6: Group work.   - AF7: Individual work.   - AF8: On-site evaluation tests. * Teaching methodologies   - MD1: Class lectures by the professor with the support of computer and audiovisual media, in which the main concepts of the subject are developed and the bibliography is provided to complement the students' learning.   - MD3: Resolution of practical cases, problems, etc. posed by the teacher individually or in groups.   - MD4: Presentation and discussion in class, under the moderation of the professor of topics related to the content of the subject, as well as case studies.   - MD5: Preparation of papers and reports individually or in groups.