Hi dear all, i am triying to do jackknife-after bootstrap for detection of
influential observation.
my data and resamples are following ;
e <- rnorm(n=50, mean=0, sd=sqrt(0.5625))
x0 <- c(rep(1,50))
x1 <- rnorm(n=50,mean=2,sd=1)
x2 <- rnorm(n=50,mean=2,sd=1)
x3 <- rnorm(n=50,mean=2,sd=1)
x4 <- rnorm(n=50,mean=2,sd=1)
y <- 1+ 2*x1+4*x2+3*x3+2*x4+e
x2[1] = 10 #influential observarion
y[1] = 10 #influential observarion
data.x <- matrix(c(x0,x1,x2,x3,x4),ncol=5)
data.y <- matrix(y,ncol=1)
replicate(3100, data.x[sample(50,50,replace=T),], simplify = FALSE)
replicate(3100, data.y[sample(50,50,replace=T),], simplify = FALSE)
now i want to calculate each of 3100 resamples's Cook's Distance like
this
formula ;
B.cap <- solve(crossprod(data.x)) %*% crossprod(data.x, data.y)
P <- data.x %*% solve(crossprod(data.x)) %*% t(data.x)
Y.cap <- P %*% data.y
e <- data.y - Y.cap
dX <- nrow(data.x) - ncol(data.x)
var.cap <- crossprod(e) / (dX)
ei <- as.vector(data.y - data.x %*% B.cap)
pi <- diag(P)
var.cap.i <- (((dX) * var.cap)/(dX - 1)) -
(ei^2/((dX - 1) * (1 - pi)))
ti <- ei / sqrt(var.cap * (1 - pi))
ti.star <- ei / sqrt(var.cap.i * (1 - pi))
pi.star <- pi + ei^2 / crossprod(e)
Ci <- (ti^2/ncol(data.x))*(pi/(1-pi)) ####(Cook's Distance)
and i want to compute each of resamples, which do not include the
influential observation, Cook's Distances. Can someone help me about this ?
Thanks for any idea..
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