前言

数学字体

\[\begin{equation} \begin{split} \mathrm{Var}(\hat{\beta}) & =\mathrm{Var}((X'X)^{-1}X'y)\\ & =(X'X)^{-1}X'\mathrm{Var}(y)((X'X)^{-1}X')'\\ & =(X'X)^{-1}X'\mathrm{Var}(y)X(X'X)^{-1}\\ & =(X'X)^{-1}X'\sigma^{2}IX(X'X)^{-1}\\ & =(X'X)^{-1}\sigma^{2} \end{split} \tag{0.1} \end{equation}\]

Let \(\mathcal{T}\) be a topological space, a basis is defined as

\[ \mathcal{B} = \{B_{\alpha} \in \mathcal{T}\, |\, U = \bigcup B_{\alpha} \forall U \in \mathcal{T} \} \]

软件信息

xfun::session_info()
## R Under development (unstable) (2019-10-05 r77257)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 8.1 x64 (build 9600)
## 
## Locale:
##   LC_COLLATE=Chinese (Simplified)_China.936 
##   LC_CTYPE=Chinese (Simplified)_China.936   
##   LC_MONETARY=Chinese (Simplified)_China.936
##   LC_NUMERIC=C                              
##   LC_TIME=Chinese (Simplified)_China.936    
## 
## Package version:
##   askpass_1.1        assertthat_0.2.1   backports_1.1.5   
##   base64enc_0.1.3    BH_1.69.0.1        bookdown_0.14     
##   broom_0.5.2        callr_3.3.2        cellranger_1.1.0  
##   cli_1.1.0          clipr_0.7.0        codetools_0.2-16  
##   colorspace_1.4-1   compiler_4.0.0     crayon_1.3.4      
##   curl_4.2           DBI_1.0.0          dbplyr_1.4.2      
##   digest_0.6.21      dplyr_0.8.3        ellipsis_0.3.0    
##   evaluate_0.14      fansi_0.4.0        forcats_0.4.0     
##   fs_1.3.1           generics_0.0.2     ggplot2_3.2.1     
##   glue_1.3.1         graphics_4.0.0     grDevices_4.0.0   
##   grid_4.0.0         gtable_0.3.0       haven_2.1.1       
##   highr_0.8          hms_0.5.1          htmltools_0.4.0   
##   httr_1.4.1         jsonlite_1.6       knitr_1.25        
##   labeling_0.3       lattice_0.20-38    lazyeval_0.2.2    
##   lifecycle_0.1.0    lubridate_1.7.4    magrittr_1.5      
##   markdown_1.1       MASS_7.3.51.4      Matrix_1.2.17     
##   methods_4.0.0      mgcv_1.8.29        mime_0.7          
##   modelr_0.1.5       munsell_0.5.0      nlme_3.1-141      
##   openssl_1.4.1      pillar_1.4.2       pkgconfig_2.0.3   
##   plogr_0.2.0        plyr_1.8.4         prettyunits_1.0.2 
##   processx_3.4.1     progress_1.2.2     ps_1.3.0          
##   purrr_0.3.2        R6_2.4.0           RColorBrewer_1.1.2
##   Rcpp_1.0.2         readr_1.3.1        readxl_1.3.1      
##   rematch_1.0.1      reprex_0.3.0       reshape2_1.4.3    
##   rlang_0.4.0        rmarkdown_1.16     rstudioapi_0.10   
##   rvest_0.3.4        scales_1.0.0       selectr_0.4.1     
##   splines_3.6.0      stats_4.0.0        stringi_1.4.3     
##   stringr_1.4.0      sys_3.3            tibble_2.1.3      
##   tidyr_1.0.0        tidyselect_0.2.5   tidyverse_1.2.1   
##   tinytex_0.16       tools_4.0.0        utf8_1.1.4        
##   utils_4.0.0        vctrs_0.2.0        viridisLite_0.3.0 
##   whisker_0.4        withr_2.1.2        xfun_0.10         
##   xml2_1.2.2         yaml_2.2.0         zeallot_0.1.0

写作环境

这本书在 RStudio 里用 R Markdown 编辑源文件,借助 bookdown (Xie 2016) 可以将 Rmd 文件组织起来, rmarkdown (Allaire et al. 2019; Xie, Allaire, and Grolemund 2018)和 knitr (Xie 2015) 将源文件编译成 Markdown 文件,Pandoc 将 Markdown 文件转化成 HTML 和 TeX 文件,用 TinyTeX 将 TeX 文件编译成 PDF 文档,所有的图形都用 ggplot2 包制作 (Wickham 2016)

本书使用的代码字体来自 Source Code Pro,可以免费使用

参考文献

Allaire, JJ, Yihui Xie, Jonathan McPherson, Javier Luraschi, Kevin Ushey, Aron Atkins, Hadley Wickham, Joe Cheng, Winston Chang, and Richard Iannone. 2019. Rmarkdown: Dynamic Documents for R. https://CRAN.R-project.org/package=rmarkdown.

Wickham, Hadley. 2016. ggplot2: Elegant Graphics for Data Analysis. Second. New York, NY: Springer-Verlag. https://doi.org/10.1007/978-3-319-24277-4.

Xie, Yihui. 2015. Dynamic Documents with R and Knitr. 2nd ed. Boca Raton, Florida: Chapman; Hall/CRC. http://yihui.name/knitr/.

Xie, Yihui. 2016. Bookdown: Authoring Books and Technical Documents with R Markdown. Boca Raton, Florida: Chapman; Hall/CRC. https://bookdown.org/yihui/bookdown.

Xie, Yihui, J. J. Allaire, and Garrett Grolemund. 2018. R Markdown: The Definitive Guide. Boca Raton, Florida: Chapman; Hall/CRC. https://bookdown.org/yihui/rmarkdown.