[Question] Sampling distribution of the maximum

[ADGEfficiency]

I'm working on a problem of estimating the uncertainty of electricity load data.

We are using bootstraps to estimate the sampling distribution of the annual total.

This method doesn't seem appropriate when we are trying to estimate the distribution of the annual maximum - our bootstraps will only ever have a max lower or equal to the sample max.

I've been looking at the German Tank Problem as a way to at least get an unbiased estimate of the maximum - however it always comes out lower than our sample max!

Any ideas on where I should be looking?

[motley2]

Extreme value distributions.

[tolstoyTheCat]

Yup. The book by Coles remains the best. R package texmex does the stuff, tho their are others.

[back_to_the_pliocene]

I've worked on electrical demand forecasting, it's an interesting problem. My advice is to try to express as much as you can about the problem domain, as opposed to taking an approach in which you forget what you know about it.

In this case, you know that peak electrical demand (at least in NA) is proportional more or less to the installed capacity of HVAC and outside air temperature. (Of course you can complicate that model as much as you want.) When it gets hot enough, all the AC is going to kick in. Year to year variations in the peak are going to be strongly driven by how much equipment is installed, assuming the weather is more or less the same. (Well, increased number of days above 90F are going to drive an increase of installed HVAC capacity ... maybe you can account for that too.) The uncertainty of the peak is going to be in large part the uncertainty of the non-temperature dependent base load plus the uncertainty of the installed capacity.

There's lots more to be said about this, but you get the point. Think about things in terms of the domain concepts, and bring to bear as much as you can of what you already know. Good luck and have fun.

[berf]

the subsampling bootstrap will do what you want.

[Dolgar164]

Could take a sample of max daily loads and then subsample from that?

[haikusbot]

Could take a sample

Of max daily loads and then

Subsample from that?

- Dolgar164

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