Math Is Fun Forum

lindah

Member

Registered: 2010-01-25

Posts: 121

MLE and its variance

Hi guys,

I am back with an annoying MLE as follows (sorry in advance for the length!!!):
http://imageshack.us/photo/my-images/199/83863226.png/

The first part requires developing an MLE for theta.

First I defined the log likelihood of this function as follows:

The differentiated it with respect to theta to obtains

Equating the above to 0 and rearranging it to obtain theta I get:

Do you guys get anything similar?

The second part requires calculating a variance for the estimator so my thoughts were to use the following rules:

where

So I used these following steps:

In the question we were given that

so I substitute this in:

substituting the estimate of theta as derived in the first part gives an answer of:

Thank you in advance for any feedback

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: MLE and its variance

Hi,

For the first part, I get the same.

I don't know the second part.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

lindah

Member

Registered: 2010-01-25

Posts: 121

Re: MLE and its variance

Hi gAr,

Thank you very much for having a look!!

The second part I've never come across before, though I get similar answers using Hessian and Fisher Information methods

Linda

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: MLE and its variance

Hi lindah,

You're welcome!

I too never came across that before. I couldn't find a similar problem either.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."