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Somers'D and ASE - dirty implementation in R

mjaniec Dec 15th, 2013 130 Never
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  1. PD    <- c(0.05,0.10,0.50,1,2,5,25)/100
  2. total <- c(5,10,20,25,20,15,5)/100
  3.  
  4. raw <- rbind(PD,total)*100
  5.  
  6. defaulted    <- total*PD
  7. nondefaulted <- total*(1-PD)
  8.  
  9. n <- sum(total)
  10.  
  11. portfolio <- rbind(defaulted,nondefaulted)/n
  12.  
  13. portfolio
  14.  
  15. ### ASE
  16.  
  17. x <- portfolio
  18.  
  19. wr <- n^2-sum(sapply(1:nrow(x), function(i) sum(x[i,])^2))
  20.  
  21. A <- function(x,i,j) {
  22.  
  23.   xr <- nrow(x)
  24.   xc <- ncol(x)
  25.  
  26.   sum(x[1:xr>i,1:xc>j])+sum(x[1:xr<i,1:xc<j])
  27.  
  28. }
  29.  
  30. D <- function(x,i,j) {
  31.  
  32.   xr <- nrow(x)
  33.   xc <- ncol(x)
  34.  
  35.   sum(x[1:xr>i,1:xc<j])+sum(x[1:xr<i,1:xc>j])
  36.  
  37. }
  38.  
  39. Pf <- function(x) {
  40.  
  41.   xr <- nrow(x)
  42.   xc <- ncol(x)
  43.  
  44.   tmp <- NULL
  45.  
  46.   for (i in 1:xr)
  47.     for (j in 1:xc)
  48.      
  49.       tmp <- c(tmp,x[i,j]*A(x,i,j))
  50.  
  51.   sum(tmp)
  52.  
  53. }
  54.  
  55. Qf <- function(x) {
  56.  
  57.   xr <- nrow(x)
  58.   xc <- ncol(x)
  59.  
  60.   tmp <- NULL
  61.  
  62.   for (i in 1:xr)
  63.     for (j in 1:xc)
  64.      
  65.       tmp <- c(tmp,x[i,j]*D(x,i,j))
  66.  
  67.   sum(tmp)
  68.  
  69. }
  70.  
  71. P <- Pf(x)
  72. Q <- Qf(x)
  73.  
  74. # ASE1
  75. tmp2 <- NULL
  76. for (i in 1:nrow(x))
  77.   for (j in 1:ncol(x))  
  78.     tmp2 <- c( tmp2, x[i,j] * ( wr*(A(x,i,j)-D(x,i,j)) - (P-Q)*(sum(x)-sum(x[i,])) )^2 )
  79.  
  80. # ASE0
  81. tmp <- NULL
  82. for (i in 1:nrow(x))
  83.   for (j in 1:ncol(x))  
  84.     tmp <- c( tmp, x[i,j]*(A(x,i,j)-D(x,i,j))^2 )
  85.  
  86. # Somers' D
  87. # -0.6839158
  88. (P-Q)/wr
  89.  
  90. # ASE1
  91. # 2.378
  92. 2/wr^2*sqrt(sum(tmp2))
  93.  
  94. # ASE0 - hypothesis of independence
  95. 2/wr*sqrt( sum(tmp)-(P-Q)^2/sum(x) )
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