One way confidence interval

Suppose I am estimating a parameter that ranges from 0 to 5. Now, suppose I obtain an estimate of 5. How do I report a confidence interval for this? An upper bound above 5 would simply not make sense. I believe this is a one-tailed test but how do I report this? Would it be (lower bound, 5)? Thanks so much!


Active Member
How did you "obtain an estimate of 5"? Do you mean all the observations were 5, hence their mean was 5? If so, you have no way to estimate variability from the data, and hence no way to obtain a frequentist confidence interval.
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Ambassador to the humans
@j58 That's not entirely true. And they said the parameter ranges from 0 to 5 - not just the data.

@leonedelman can you provide some more info about your data, your model, and what you're trying to do?


Omega Contributor
This is likely similar to when people have data comprised of percentages and get a parameter of say 99%, it is contained {0,1}, so it is has an asymmetrical CIs with top bound at 5. It is definitely not a one-sided confidence interval. An easy thing may be to scale data between 0-1 and use the existing calculations out there. Another option may be using a 95% bootstrap confidence interval.