Finding estimated standard error.

Let $\displaystyle X_{1},...,X_{n}$ ~ F and let $\displaystyle \hat{F}$ be the empirical distribution function.

Let a<b fixed numbers, define θ = T(F) = F(b) − F(a). Let θˆ = T(Fˆn) = Fˆn(b) − Fˆn(a).

Find the estimated standard error of θ.

So... I am not sure how to approach this correctly.

Am I supposed to find sample error of the sample mean se($\displaystyle \hat\mu$)=$\displaystyle \hat\sigma$/$\displaystyle n^(0.5)$ and then use this for estimated SE?

and then use the Var of empirical dstbn for Fˆn(b) − Fˆn(a)?

any help is appreciated as I don't know which road to take.

Re: Finding estimated standard error.

Hey farmeruser1,

Can you outline how to calculate theta as a function of your sample?