I have a question regarding the interpretation of the tsboot call in R. I checked the documentation of both the Kendall and the boot package, but am no smarter than before.
When I run a bootstrap using e.g. the example in the Kendall package, where the test statistic is Kendall's tau:
library(Kendall) # Annual precipitation entire Great Lakes # The Mann-Kendall trend test confirms the upward trend. data(PrecipGL) MannKendall(PrecipGL)
which confirms the upward trend:
tau = 0.265, 2-sided pvalue =0.00029206
The example then continues to use a block bootstrap:
# #Use block bootstrap library(boot) data(PrecipGL) MKtau<-function(z) MannKendall(z)$tau tsboot(PrecipGL, MKtau, R=500, l=5, sim="fixed")
I receive the following result:
BLOCK BOOTSTRAP FOR TIME SERIES Fixed Block Length of 5 Call: tsboot(tseries = PrecipGL, statistic = MKtau, R = 500, l = 5, sim = "fixed") Bootstrap Statistics : original bias std. error t1* 0.2645801 -0.2670514 0.09270585
If I understand correctly, the "t1* original" is the original MKtau, the "bias" is the mean of the MKtau from the R=500 bootstrapped time series, and the "std. error" is the standard deviation of the MKtaus from the 500 samples.
I have trouble understanding what this means - this basically tells me that all 500 MKTaus are lower than the original, and that the original t1* is in the range of 3 sd of the bootstrapped MKtaus. Ergo it is significantly different?
Or would I say the MKtau for the data set is 0.26 plus/minus standard error?
I'm sorry for the lengthy question, but I am a statistics novice and am learning via self-study, lacking someone to bounce this probably really simple problem back and forth with.