An introduction to statistics - theory and practice

PART 1

There are plenty of references on Part 1, see for instance

• https://ocw.mit.edu/courses/18-655-mathematical-statistics-spring-2016/

• https://math.emory.edu/~lchen41/teaching/2020_Spring/Larsen-5E.pdf

• https://online.stat.psu.edu/stat415/

PART 2

Here are enclosed some references on Part 2

• STAT 2150 (density)
• Ferraty and Vieu (regression)

To go further:

• https://faculty.washington.edu/yenchic/17Sp_403/Lec7-density.pdf
• https://www.stat.cmu.edu/~larry/=stat705/Lecture26.pdf
• https://www.nbi.dk/~koskinen/Teaching/AdvancedMethodsInAppliedStatistics2019/Lecture8_KDE.pdf
• http://csyue.nccu.edu.tw/ch/Kernel%20Estimation(Ref).pdf
• https://users.ssc.wisc.edu/~bhansen/718/NonParametrics1.pdf
• https://towardsdatascience.com/the-math-behind-kernel-density-estimation-5deca75cba38/
• https://bookdown.org/egarpor/PM-UC3M/npreg-kre.html
• https://bookdown.org/mike/data_analysis/sec-kernel-regression.html
• https://faculty.washington.edu/yenchic/18W_425/Lec9_Reg01.pdf

• Ferraty, F. and Vieu, P. (2006) Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics). Springer-Verlag, Berlin.

• Yandell, B. S. (1996). Kernel Smoothing. Technometrics, 38(1), 75–76. https://doi.org/10.1080/00401706.1996.10484419

• Chacón, J.E., & Duong, T. (2018). Multivariate Kernel Smoothing and Its Applications (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9780429485572

• on the software, you can try to apply to any data and adapt the code we have done 
• on a sheet of paper... It seems very difficult for me to do this... a few examples: proove that the kernel estimator of a density is a density, compute the efficiencies of the different kernels,...

Here are all the datasets we will consider (in addition to those already included in R) 

For an interactive document, please have a look to https://laurent-delsol-idp.shinyapps.io/TP_DEN/

For an interactive document have a look to https://laurentdelsol.shinyapps.io/TP_REG/