+ Reply to Thread
Results 1 to 1 of 1

Thread: bridge estimation in linear regression

  1. 11-25-2010 10:53 PM #1
    zzzc
    zzzc is offline
    Points: 3,017, Level: 33
    Level completed: 78%, Points required for next Level: 33
    Posts
    41
    Thanks
    0
    Thanked 0 Times in 0 Posts

    bridge estimation in linear regression



    So the bridge estimates, \beta (which is a vector of \beta_1,...,\beta_p), minimize
    \sum_{i=1}^n (y_i - x_i^T\beta)^2 + \lambda\sum_{j=1}^p(\left\vert \beta_j \right\vert )^\gamma)
    It is suggested that we can implement the function
    g(x) = x^2 - 2ax + b\left\vert x\right\vert^c

    I can see that we can substitute x with \beta_j , b with \lambda , c with \gamma

    But the first part
    (y_i - x_i^T\beta)^2 is not clear to me how I can implement so that it'll look like
    x^2 - 2ax

    Can someone help to derive this?
    Thanks!!
    Last edited by zzzc; 11-25-2010 at 11:39 PM.
    Reply With Quote Reply With Quote
+ Reply to Thread
« how to calculate Factor Scores? | Project ideas »

Similar Threads

  1. R^2 for linear multiple linear regression
    By raver_68 in forum Regression Analysis
    Replies: 5
    Last Post: 05-12-2010, 04:25 PM
  2. linear model estimation: how many regressors to choose?
    By vadim1508_1 in forum Psychology Statistics
    Replies: 3
    Last Post: 04-19-2009, 09:33 PM
  3. estimation for a particular type of heteroscedastic regression
    By shoomchool in forum Psychology Statistics
    Replies: 1
    Last Post: 10-17-2008, 03:06 PM
  4. Regression Analysis Non linear estimation using squares
    By vladinator in forum Regression Analysis
    Replies: 1
    Last Post: 04-30-2007, 09:01 PM
  5. Multiple regression least square estimation
    By byip in forum Regression Analysis
    Replies: 0
    Last Post: 05-20-2006, 11:44 AM

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts

Forum Rules








Advertise on Talk Stats