# Bootstrap: estimate is outside of confidence interval

I did a bootstrapping with a mixed model (several variables with interaction and one random variable). I got this result (only partial):

> boot_out

ORDINARY NONPARAMETRIC BOOTSTRAP

Call:
boot(data = a001a1, statistic = bootReg, R = 1000)

Bootstrap Statistics :
original        bias     std. error
t1*   4.887383e+01 -1.677061e+00 4.362948e-01
t2*   3.066825e+01  1.264024e+00 5.328387e-01
t3*   8.105422e+01  2.368599e+00 6.789091e-01
t4*   1.620562e+02  4.908711e+00 1.779522e+00
......


Now, I wanted to get the confidence intervals for the intercept:

> boot.ci(boot_out,type=c("norm","basic","perc"), index=1)
BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 1000 bootstrap replicates

CALL :
boot.ci(boot.out = boot_out, type = c("norm", "basic",
"perc"), index = 1)

Intervals :
Level      Normal              Basic              Percentile
95%   (49.70, 51.41 )   (49.70, 51.41 )   (46.34, 48.05 )
Calculations and Intervals on Original Scale


The bias corrected estimated is:

48.873 -1.677
1 47.196

The problem I have is that the normal and basic CI are outside of the estimate (original and corrected). I just wonder how to cope with that.

Update 1:
Here is a similar questions with a lot of responses.

• Just a comment: Efron & Tibshirani (1993) in the classic book were arguing rather against bias correction saying it is a "dangerous" and "problematic" practice that could lead to increased standard error. – Tim Feb 2 '15 at 11:07
• @Tim Thanks for your comment. I will have a look at the book. Maybe, a solution is to use the estimates and and the bootstrap se* to compute the confidence intervals. In my case, the bias affect the estimates only slightly. – giordano Feb 2 '15 at 13:08