Peter Dalgaard
@pdalgd.bsky.social
2.5K followers 201 following 3.8K posts
Statistics in general, #rstats in particular (Core team member). Professor at CBS w/biostats background. Likes cooking and bicycling and socialising in general. Oh, and music: Opera, Jazz, ProgRock.
![# minor gotcha, sometimes important:
sum(acf(x, plot=F, lag.max=19)$acf) # always = 0.5
# ..because 0 = (sum_i Z_i)^2 = sum_i Z_i^2 + 2 * sum_(i < j) Z_i Z_j
# sum_i Z_i^2 = n & sum_(i < j) Z_i Z_j = sum_j n*rho_j
n <- 5
x <- rnorm(n)
xm <- x - mean(x)
z <- xm/sqrt(sum(xm^2)/n)
V <- outer(z,z)
V
round(sum(V),5) # zero
sum(diag(V)) # n so sum of off-diag elements must be -n
diag(V[,-(1:2)])
sum(diag(V[,-(1:2)]))/n # alias rho_2
acf(x, plot=FALSE, lag.max=4)](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:ikqayrfeyprhhhqoyinfoauj/bafkreidj6q3jvwt67dqbbsnisfajcmi3dw7gdrihjxtxl3ns673snpoixm)
