Timeline for Confidence interval for parameter in uniform distribution using MOM estimator
Current License: CC BY-SA 3.0
9 events
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| Apr 11, 2018 at 3:59 | comment | added | Glen_b | The CLT itself proves asymptotic normality of a standardized $\bar{X}$. If the conditions of the CLT hold, surely you can simply invoke it rather than prove it. If you didn't want to rely on an asymptotic argument (since you don't actually have $n\to\infty$, but some particular $n$), you could use one or another inequality to bound the error in the normal approximation of the cdf. However with n=100 the sample mean of uniforms will work very well if you don't go into the extreme tail. | |
| Apr 10, 2018 at 21:21 | comment | added | eliott | @rannoudanames, do I need to check/prove asymptotic normality so that I can apply CLT to use z? | |
| Apr 10, 2018 at 20:03 | vote | accept | eliott | ||
| Apr 10, 2018 at 20:00 | comment | added | rannoudanames | @jbowman Thx for insight! | |
| Apr 10, 2018 at 19:59 | history | edited | rannoudanames | CC BY-SA 3.0 |
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| Apr 10, 2018 at 19:58 | comment | added | jbowman | Yes, we can, but it's still an asymptotic approximation. With $N=100$, it's going to be a really, really good approximation! And, since the OP asks for a 90% asymptotic confidence interval, I'd just modify my answer slightly and go with it. | |
| Apr 10, 2018 at 19:55 | comment | added | rannoudanames | @jbowman In that case can't we simply use normal? But overall approach still holds correct? | |
| Apr 10, 2018 at 19:42 | comment | added | jbowman | The $t$ distribution isn't true, it's an approximation that becomes quite accurate as the sample size grows - in fact, it's already fairly accurate (in some informal sense of the word) for $N = 30$ in the case of the Uniform distribution. Note also that we know the population variance exactly, it's $1/12$, so don't need to rely on the sample standard deviation (nor, consequently, on the $t$ distribution at all.) | |
| Apr 10, 2018 at 19:09 | history | answered | rannoudanames | CC BY-SA 3.0 |