Timeline for Interpretation of a 95% confidence interval calculated via bootstrapping?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 29, 2015 at 10:45 | comment | added | Glen_b | And now we've come back to my very first paragraph in my answer. How does using bootstrapping to obtain the interval make a difference to what the interval means? | |
| Jun 29, 2015 at 10:18 | comment | added | luciano | Ok, so bootstrapping simply tells us what the sampling distribution of the point estimate would look like if we were to repeatedly sample. But despite trying hard, I can't see how this definition of a confidence interval is wrong; "there is a 95% probability the confidence interval contains the population parameter" | |
| Jun 29, 2015 at 10:00 | comment | added | Glen_b | Let's come at this from another angle. How are you (luciano, not Maarten) going to generate a CI from each resample without making some distributional assumption? | |
| Jun 29, 2015 at 9:56 | comment | added | Maarten Buis | With the bootstrap you do not estimate the interval in each replication but the point estimate. It is the distribution of these point-estimates that is an estimate of the sampling distribution of the point estimates. From that you derive the lower and upper bounds of your confidence interval, which has exactly the same interpretation as the confidence interval estimated by other means. | |
| Jun 29, 2015 at 9:47 | comment | added | luciano | I thought that was the point of bootstrapping: to pretend the sample is the population and repeatedly take new samples from the population | |
| Jun 29, 2015 at 9:43 | comment | added | Glen_b | Resampling from your sample is not getting a new sample of the population. | |
| Jun 29, 2015 at 9:40 | comment | added | luciano | In the below link, this is how the definition of a confidence interval begins: "It means that if the same population is sampled on numerous occasions and interval estimates are made on each occasion…". This definition suggests to me that we should use the standard errors of each resampleto calculate a confidence interval and there is a 95% probability each confidence interval contains the population parameter. itl.nist.gov/div898/handbook/prc/section1/prc14.htm | |
| Jun 29, 2015 at 9:17 | comment | added | Glen_b | The point of bootstrapping a CI is to generate an interval without relying on a distributional assumption; (i) how are you going to get an interval from a single resample; and (ii) how will having 10000 intervals help you find out the coverage properties? | |
| Jun 29, 2015 at 7:26 | comment | added | luciano | I'm still struggling! If we resample 10,000 times, why don't we calculate 10,000 confidence intervals? | |
| Jun 29, 2015 at 6:31 | history | answered | Glen_b | CC BY-SA 3.0 |