Lecture-notes

This is a Lecture note of courses that I took recently in my Ph.D. in statistics.

Chapter 1: High-dimensional statistics

This Chapter is based on Spring 2022 STAT 946 - Topics in Statistics: High dim in Statistics (Instructor: Dr. David Saunders, Adam Kolkiewicz) and STAT 946 Fall 2021 (Instructor: Dr. Aukosh Jagannath) at UWaterloo.

References:

• \item Martin J. Wainwright, High-Dimensional Statistics \cite{wainwright_2019}
• \item High Dimensional Statistics Lecture Notes, Philippe Rigollet and Jan-Christian H"utte. \footnote{\url{https://klein.mit.edu/~rigollet/PDFs/RigNotes17.pdf}}
• \item Roman Vershynin, High-Dimensional Probability \footnote{\url{https://www.math.uci.edu/~rvershyn/papers/HDP-book/HDP-book.pdf}}
• \item Ramon van Handel, Probability in High Dimension \footnote{\url{https://web.math.princeton.edu/~rvan/APC550.pdf}}
• \item Christophe Giraud, Introduction to High-Dimensional Statistics \footnote{\url{https://www.imo.universite-paris-saclay.fr/~giraud/Orsay/Bookv3.pdf}}
• \item Alexandre B. Tsybakov, Introduction to Nonparametric Estimation \footnote{\url{https://link.springer.com/book/10.1007/b13794}}
• \item A. S. Bandeira, A. Singer, T. Strohmer, Mathematics of Data Science \footnote{\url{https://people.math.ethz.ch/~abandeira/BandeiraSingerStrohmer-MDS-draft.pdf}}

Chapter 2: Statistical inference

This Chapter is based on STAT 908 Statistical Inference (Instructor: Dr. Pengfei Li) at UWaterloo.

References:

• \item Mathematical statistics by Jun shao \cite{Shao_2003_book}
• \item Theoretical Statistics: Topics for a Core Course by R. Keener. \cite{keener2010theoretical}
• \item Asymptotic Statistics by A. W. van der Vaart
• \item \cite{RefWorks27doc61c73dd48f083801efa8afc4} \url{https://arxiv.org/pdf/2010.14863}
• \item Reference lists \cite{montanari2020mean} \url{https://web.stanford.edu/~montanar/OTHER/TALKS/oops_refs.pdf}

Chapter 4: Probability

This Chapter is based on STAT 902 - Theory of Probability 2 (Instructor: Dr. Yi shen) at UWaterloo.

References:

• \item Amir Dembo, Probability Theory: STAT310/MATH230 (April 15, 2021)\footnote{\url{https://statweb.stanford.edu/~adembo/stat-310b/lnotes.pdf}}
• \item Jean-Francois Le Gall, Brownian Motion, Martingales, and Stochastic Calculus\footnote{\url{https://link.springer.com/book/10.1007/978-3-319-31089-3}}
• \item Timo Seppalainen, Basics of Stochastic Analysis \footnote{\url{https://www.math.wisc.edu/~seppalai/courses/735/notes.pdf}}
• \item Rick Durrett, Theory and Examples (Version 5) \footnote{\url{https://services.math.duke.edu/~rtd/PTE/PTE5_011119.pdf}} * \item John B. Walsh, Knowing the Odds: An Introduction to Probability\footnote{\url{https://bookstore.ams.org/gsm-139}}
• \item Bernt Oksendal, Stochastic Differential Equations \footnote{\url{https://link.springer.com/book/10.1007/978-3-642-14394-6}}