I am truncating the slope (not the data). So if I know the true value of
the slope is beta which should be in the interval (0,1). How do I prove
that a truncated slope. That is the following:
betahat_new = 0, if betahat<0
betahat, 0<betahat<1
1 if betahat >1
is an unbiased estimator of the slope?
Reacll beta is the slope of a simple linear regression and the errors are
independent but not identical. The x's are constants. Any ideas?
Jim
2011/12/4 John Bibby <[log in to unmask]>
> Basilio's suggestion is good. Have you considered transforming the
> parameter e.g.using Box & Cox so that it covers the whole range +-
> infinity? Then you could use standard methods.
>
> JOHN BIBBY
>
> 2011/12/4 Basilio de Bragança Pereira <[log in to unmask]>:
> > See
> > Restrict least square or constrained maximum likelihood estimator in
> > econometric textbook
> > or for example pages like
> > http://www.maths.usyd.edu.au/u/jchan/GLM/RestrictedLeastSquares.pdf
> >
> > Basilio
> >
> > 2011/12/3 John Sorkin <[log in to unmask]>
> >
> >> Independent of whether your result converges to the true slope, you will
> >> have inferential problems as your estimator will not be normally
> >> distributed.
> >> John
> >>
> >> John David Sorkin M.D., Ph.D.
> >> Chief, Biostatistics and Informatics
> >> University of Maryland School of Medicine Division of Gerontology
> >> Baltimore VA Medical Center
> >> 10 North Greene Street
> >> GRECC (BT/18/GR)
> >> Baltimore, MD 21201-1524
> >> (Phone) 410-605-7119
> >> (Fax) 410-605-7913 (Please call phone number above prior to faxing)
> >>
> >> >>> Jim Silverton <[log in to unmask]> 12/3/2011 12:51 PM >>>
> >> Hello all,
> >>
> >> I am interested in doing the following. I have a simple linear
> regression
> >> problem: Y = a + bX + e where e are errors not necessarily. Now the
> truth
> >> is that the true slope is between 0 and 1. But my regression equation
> gives
> >> me a slope that can be either be negative, or positive. So I truncate
> the
> >> slope, meaning if I get a negative value for the slope, I use 0 and if I
> >> get a positive value greater than 1, I use 1.
> >>
> >> My question is this are there any papers around that has this proof for
> >> this type of truncation of the slope? I am looking for a proof that the
> >> trimmed slope that I am using actually converges to the true slope.
> >>
> >> --
> >> Thanks,
> >> Jim.
> >>
> >> You may leave the list at any time by sending the command
> >>
> >> SIGNOFF allstat
> >>
> >> to [log in to unmask], leaving the subject line blank.
> >>
> >> Confidentiality Statement:
> >> This email message, including any attachments, is for the sole use of
> the
> >> intended recipient(s) and may contain confidential and privileged
> >> information. Any unauthorized use, disclosure or distribution is
> >> prohibited. If you are not the intended recipient, please contact the
> >> sender by reply email and destroy all copies of the original message.
> >>
> >> You may leave the list at any time by sending the command
> >>
> >> SIGNOFF allstat
> >>
> >> to [log in to unmask], leaving the subject line blank.
> >>
> >
> >
> >
> > --
> >
> > Basilio de Bragança Pereira ,DIC and PhD(Imperial College), DL(COPPE)
> > *UFRJ-Federal University of Rio de Janeiro
> > *Titular Professor of Bioestatistics and of Applied Statistics
> > *FM-School of Medicine and COPPE-Posgraduate School of Engineering and
> > HUCFF-University Hospital Clementino Fraga Filho.
> >
> > *Tel: 55 21 2562-7045/7047/2618/2558
> > www.po.ufrj.br/basilio/
> >
> > *MailAddress:
> > COPPE/UFRJ
> > Caixa Postal 68507
> > CEP 21941-972 Rio de Janeiro,RJ
> > Brazil
> >
> > You may leave the list at any time by sending the command
> >
> > SIGNOFF allstat
> >
> > to [log in to unmask], leaving the subject line blank.
>
> You may leave the list at any time by sending the command
>
> SIGNOFF allstat
>
> to [log in to unmask], leaving the subject line blank.
>
--
Thanks,
Jim.
You may leave the list at any time by sending the command
SIGNOFF allstat
to [log in to unmask], leaving the subject line blank.
|