This repo contains the codes, images, report and slides for the first project of the course - MTH673A: Robust Statistical Methods at IIT Kanpur during the academic year 2022-2023.

Project Members:

• Arkajyoti Bhattacharjee
• Rachita Mondal
• Ritwik Vashishtha
• Shubha Sankar Banerjee

Project Title:

Understanding Nonparametric Modal Regression via Kernel Density Estimation [Report] [Slides]

Abstract:

In this report we review non-parametric Modal Regression using Kernel Density Estimator. Instead of using conditional mean, Modal Regression uses conditional mode to summarize the relationship between the response and the explanatory variables. We describe the idea of Modal Regression and include a brief discussion regarding the superiority of Multi-modal regression over the Uni-modal case. The consistency properties of the proposed estimator and the idea of Confidence Sets have been reviewed. This report also includes an application of Prediction Sets in case of Bandwidth selection. Certain generalizations and extensions are also discussed. The report is primarily based on Chen, Y. C., Genovese, C. R., Tibshirani, R. J., & Wasserman, L. (2016). Nonparametric modal regression. The Annals of Statistics, 44(2), 489-514.

Table of Contents:

Section	Topic
1	Introduction
2	Modal Regression 2.1. Uni-modal vs. Multi-modal Regression
3	Estimation 3.1. Mean-shift Algorithm
4	Geometric Properties
5	Consistency
6	Confidence Sets
7	Prediction Sets 7.1. Bandwidth Selection
8	Discussion
9	Supplementary Material
10	Acknowledgements

Primary References:

1. Chen, Y. C., Genovese, C. R., Tibshirani, R. J., & Wasserman, L. (2016). Nonparametric modal regression. The Annals of Statistics, 44(2), 489-514.
2. Chen, Y. C. (2018). Modal regression using kernel density estimation: A review. Wiley Interdisciplinary Reviews: Computational Statistics, 10(4), e1431.
3. http://faculty.washington.edu/yenchic/Talks/YC2015_JSM.pdf
4. https://github.com/yenchic/ModalRegression