Just one sec...
Hey! Sign in to get help with your study questionsNew here? Join for free to post

Cramer-Rao Lower Bound

Announcements Posted on
Take our short survey, £100 of Amazon vouchers to be won! 23-09-2016
    • Thread Starter
    Offline

    0
    ReputationRep:
    Hi everyone

    Just a quick question... you know the Cramer Rao Lower bound gives a lower bound for the variance of the statistic T(X) (being greater than or equal to 1/fisher info number).

    Why is this useful?

    Surely if anything, we want an upper bound to see the highest it's going to vary?

    I know my logic is incorrect so please can someone explain what's going on?
    Offline

    2
    I don't know anything about this thing in particular, but it's always useful to know bounds (upper and lower) for things when you can't work out their value exactly. If you have a lower bound on the variance, then you know that the data has to be spread out at least to some extent (i.e. if the lower bound is greater than zero, then you know that the data is spread out over some range and isn't just concentrated at a point).
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by nuodai)
    I don't know anything about this thing in particular, but it's always useful to know bounds (upper and lower) for things when you can't work out their value exactly. If you have a lower bound on the variance, then you know that the data has to be spread out at least to some extent (i.e. if the lower bound is greater than zero, then you know that the data is spread out over some range and isn't just concentrated at a point).
    Thanks for the advice. That was my vague intuition, however I'da thought it'd be more useful to know the maximum possible variance an estimator could achieve as opposed to the lowest. If we only have a lower bound does this provide us with "useful" information?

    For example if it was an upper bound then couldn't you intuitively tell that it was estimating accurately to within some range?

    I don't know - I'm sorry for being silly it's all just beyond me if I'm entirely honest! :confused:
    Offline

    2
    (Original post by jamesair99)
    Thanks for the advice. That was my vague intuition, however I'da thought it'd be more useful to know the maximum possible variance an estimator could achieve as opposed to the lowest. If we only have a lower bound does this provide us with "useful" information?

    For example if it was an upper bound then couldn't you intuitively tell that it was estimating accurately to within some range?

    I don't know - I'm sorry for being silly it's all just beyond me if I'm entirely honest! :confused:
    It doesn't really matter which is more useful than the other, because they're both useful :p: As a completely off-the-whim example, suppose you're working for a fire department in a hot country, and you're looking at the incidence of forest fires over the course of a year. You want to know where to concentrate your funding so that your resources are used efficiently (e.g. you don't need too much water to put out fires in January, but you do in July). If you have a mean and a lower bound for the variance of the dates when the forest fires occur, then you can work out an absolute minimum amount of resources you put in (e.g. providing enough water to put out fires between 11th June and 3rd September) and so you can budget accordingly. Having an upper bound in this case is also useful because it will tell you when the resources you provide are unnecessary, but if you didn't have a lower bound you'd run the risk of your whole country burning to a crisp.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by nuodai)
    It doesn't really matter which is more useful than the other, because they're both useful :p: As a completely off-the-whim example, suppose you're working for a fire department in a hot country, and you're looking at the incidence of forest fires over the course of a year. You want to know where to concentrate your funding so that your resources are used efficiently (e.g. you don't need too much water to put out fires in January, but you do in July). If you have a mean and a lower bound for the variance of the dates when the forest fires occur, then you can work out an absolute minimum amount of resources you put in (e.g. providing enough water to put out fires between 11th June and 3rd September) and so you can budget accordingly. Having an upper bound in this case is also useful because it will tell you when the resources you provide are unnecessary, but if you didn't have a lower bound you'd run the risk of your whole country burning to a crisp.
    Thank you very much, you're brilliant at explaining things and that example makes a lot of sense! :cool:

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. Oops, you need to agree to our Ts&Cs to register
  2. Slide to join now Processing…

Updated: December 31, 2010
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Poll
Who will be the next permanent England boss?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read here first

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22

Registered Office: International House, Queens Road, Brighton, BN1 3XE

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.