1. ## Absolute Loss Function

I am quite honestly at an "absolute loss" with this one... I know the answer can't be 2 yet I keep getting it.. any help is much appreciated.

Question:

A reinsurer decides to use a continuous uniform distribution on the interval (0,θ) to model a claim size X. She wishes to estimate θ on the basis of a single observation X and using a decision function of the form d(X) = kX. If the loss incurred is proportional to the absolute value of the error, find the value of k which minimises the (expected) risk.

2. ## Re: Absolute Loss Function

What have you do so far? How do you know the answer can't be 2? (it isn't 2 but how do you know that?)

3. ## Re: Absolute Loss Function

I am not very sure about the question, does it mean you need to find

You can calculate first by integration:

Spoiler:

And you can show that the function is strictly decreasing in the first region and should have a global minimum at .

4. ## The Following User Says Thank You to BGM For This Useful Post:

MathMaster135711 (12-03-2016)

5. ## Re: Absolute Loss Function

Originally Posted by BGM
I am not very sure about the question, does it mean you need to find

You can calculate first by integration:

Spoiler:

And you can show that the function is strictly decreasing in the first region and should have a global minimum at .
SHHHHHHHH!!! How can we expect them to learn if we just give the answer?

6. ## The Following User Says Thank You to Dason For This Useful Post:

MathMaster135711 (12-05-2016)

7. ## Re: Absolute Loss Function

I thought it is just a calculus question once we know the definition of the loss functions etc. Providing the final answer for checking purpose only and requiring OP to fill up the entire calculation process.

Ok I admit that it will not be good for OP to copy if this is just a multiple choice question.

8. ## Re: Absolute Loss Function

My guess is that they're missing the 1/k term at the end so they end up with (2/k - 1) as the multiplier which is why they keep coming up with k=2 for the answer.

9. ## The Following User Says Thank You to Dason For This Useful Post:

MathMaster135711 (12-03-2016)

10. ## Re: Absolute Loss Function

Originally Posted by BGM
I am not very sure about the question, does it mean you need to find

You can calculate first by integration:

Spoiler:

And you can show that the function is strictly decreasing in the first region and should have a global minimum at .

Originally Posted by Dason
My guess is that they're missing the 1/k term at the end so they end up with (2/k - 1) as the multiplier which is why they keep coming up with k=2 for the answer.
How does one get the 1/k term at the end? Thanks!

11. ## Re: Absolute Loss Function

Originally Posted by Dason
My guess is that they're missing the 1/k term at the end so they end up with (2/k - 1) as the multiplier which is why they keep coming up with k=2 for the answer.

So where is the extra term coming from ?! Any help at all?!

12. ## Re: Absolute Loss Function

Your first equality isn't true - you can't ignore the absolute value bars around the quantity. Like BGM said this one isn't too bad to do if you just integrate directly. You'll need to break the integral into two pieces to get rid of the absolute value (hint: break it up where KX = theta)

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