I need to test the null hypothesis that my steady returns have a zero skewness with a confidence level of 95%. Do you have any ideas which formula I can take for this kind of test ? I tried the Agostino test for skewness, but think it's not the best way, because I can't set a confidence level.
library(moments)
?agostino.test
If I understand your question correctly, all you have to do is compare the p-value from agostino.test() (which can be extracted from the returned object) with a specified alpha, i.e.
library(moments)
set.seed(1234)
x <- rnorm(1000)
a <- agostino.test(x)
a$p.value < 0.05 ## FALSE, fail to reject
(In case it's not clear, the 0.05 here is 1-(your confidence level)=1-0.95.) Or to simulate a case where the null hypothesis is false:
y <- rexp(1000,1)
agostino.test(y)$p.value < 0.05 ## TRUE, reject
Here is an example taken from https://www.statmethods.net/advstats/bootstrapping.html I made a small modification to use the skew statistic. You don't provide a data set, so I just used the one in the example on the web page reference.
The following shows and example of getting a confidence interval for a skew statistic. You can test a hypothesis using a CI if you check to see if the null value is in the confidence interval.
library(boot)
skew_f <- function(data, indices) {
d <- data[indices] # allows boot to select sample
return(e1071::skewness(d))
}
# bootstrapping with 1000 replications
results <- boot(data=faithful$eruptions, statistic=skew_f,
R=1000)
boot.ci(results, type="bca")
