Statistics Note
Recent Version Updated @ 2024/Sept/20. Fixed some typos.
Version Updated @ 2023/June/24. Almost the final version. Later updates will be minor (e.g. fixing some typos, adding links, etc.).
此外，我在树洞上进行了关于统辅课程的测评，以及一些课程先修关系建议，有兴趣的同学可以前往 树洞帖子 查看。
A Brief Summary of Statistics Minor Courses | Project on GitHub
The statistics course summary actually started from the exam cheetsheets during my first year in minor. At first it only contained some notion explanation / important results. Later I began to add mathematical deductions, intuition of methods, useful external links, etc. LaTeX is used to compile so that I could include cross reference, citation, index in the note so that I could look something up in case of forgetting. Also I treat it as an opportunity to practice LaTeX.
Since it’s written as a reminder, I may not contain some basic knowledge like calculus, linear algebra, etc. Besides, for consistency within file and familiarity for myself, I might not use some commonly used notations (An example may be the size of designed matrix. I use \(n\times (p+1)\) while some others use \(n\times p\)). Please check the denotation section in the case of confusion.
这份课程笔记是我在 清华大学统计学辅修课程 中所有课程的笔记总结。这份笔记是从初概/统推课的考试cheatsheet发展而来的，之后经过几轮完善&不断加入新课的笔记逐步成为了现在的笔记系列，每一个章节对应着统辅里的一门课，其中囊括了一些重要的知识点、容易令人困惑的问题、我自己的一些迷思、实用外链等内容。
在排版上的基本思想是便于查阅而不是便于学习，所以章节内的内容顺序很多都与统辅课上稍有不同，改成了我比较喜欢/习惯的组织模式，章节顺序也是简单地按照我上课的顺序排列。为了弥补排版顺序对内容切割的影响，文中提供了交叉引用、文末提供了索引，方便在知识之间进行链接。在具体内容上，在源头上这是应用统计学辅修课程笔记的整理，所以很多时候一些背景知识我不一定会提及，同时出于我自己的习惯或行文的一致性，有时候我习惯的记号会:
- 和通用的记号不完全一致，如回归中的设计矩阵维度我喜欢用\(n\times (p+1)\)，正态分布上分位数我喜欢用\(N_{\alpha }\)；
- 有时候引入一些我在物理专业中已经熟悉的记号，如涉及态的内积用\(\langle\)bra\(\vert\) \(\vert\)ket\(\rangle\)，Fourier用 \(\fallingdotseq\)；
- 与课程幻灯片不同
所以有时候结论可能与你习惯的版本有一些出入，不要太惊讶。如果遇到困惑可以查询笔记中的记号表章节。
Announcement
另外，我在考虑将这份东西译成中文，方便一些没有那么习惯使用英语的同学/刚入门统计需要一些中英对照的同学阅读，同时也对内容进行一些充实，如果有人有兴趣加入/也有想要分享的板块/有任何建议欢迎 联系我。
Acknowledgments
The project is mostly based on the course content of statistics minor in Center of Statistical Science at Tsinghua. I would like to express my gratitude to the faculty for their careful preparation and for their help to me. They include (in the order I first took their courses): Wanlu Deng, Jiangdian Wang, Zaiying Zhou, Dong Li, Tianying Wang, Sheng Yu, Pengkun Yang.
In particular, I would like to express my appreciation to Professor Zaiying Zhou for her guidance, encouragement and inspiration, which are largely the driving force for my further study into the field of statistics.
I would like to thank Suqing Liu for his invaluable contributions to ZH translation in this project. And I would like to thank my classmates Mai Zhang, Hao Meng and Yong Qin, who offered me help by discussing problems with me, proofreading the draft and tackling capstone projects together. I really learned a lot from them, both in knowledge and the way they learn.
本项目的内容基于 清华大学统计学辅修课程 的课程内容。首先我想向统辅课的课程教师们表示感谢，他们包括（按我第一次上课的时间顺序）：邓琬璐、王江典、周在莹、李东、王天颖、俞声、杨朋昆。特别地，我想向周在莹老师表示特别感谢，她在我统辅课期间提供了无私的指引、鼓励和激励，并很大程度上让我决定在统计学领域继续深修。感谢 刘苏青 参与到汉化工作中。另外我还想感谢我的课友章迈、孟灏、秦勇，他们常在课后与我讨论学术问题并给予我各种帮助。