Results 1 to 1 of 1

Math Help - Variance of beta when estimating a censored variable using OLS

  1. #1
    Newbie
    Joined
    Jan 2011
    Posts
    1

    Variance of beta when estimating a censored variable using OLS

    Hi!
    I have this statistical problem that has been bugging me for quite a while, and I would be extremly grateful if someone would be kind enough to help me.

    Given this set-up:
    y= c if y*>c
    xiB+e if y*<c

    where B= Beta
    e= Epsilon


    What is the variance of B when using OLS-estimation?

    Note: I've attached a pdf with the equations below, where the numbering is the same, if that is preferred.

    What I've been able to derive thus far is the following:
    V(B)= sum[(xi^2/((sum(xi^2))^2) * V(yi) (1)

    Using the law of total variance V(yi) should be:
    V(yi)= V(E[yi|x]) + E(V[yi|x]) (2)

    Where:
    E(V[yi|xi])= V(c) * P(y*>c) + V(xiB+e) * P(y*<c) (3)
    = Sigma^2 * P(y*<c) (4)

    PROBLEM: Assuming my expression for E(V[yi|xi]) is correct, what does the expression for V(E[yi|x]) look like?
    Attached Thumbnails Attached Thumbnails Variance of beta when estimating a censored variable using OLS-equations.pdf  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 2nd 2012, 11:39 PM
  2. Deriving expected value and variance of beta distribution
    Posted in the Advanced Statistics Forum
    Replies: 11
    Last Post: February 14th 2011, 11:32 PM
  3. mean and variance of a beta distribution
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 9th 2010, 01:47 PM
  4. beta random variable
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 4th 2009, 04:03 AM
  5. Proving Beta Distribution Variance
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 14th 2008, 01:43 PM

Search Tags


/mathhelpforum @mathhelpforum