Dear Jim,
When you assume slope parameter is less than 1 (in absolute value ), and
some influential observations make the slope estimator greater than 1, You
can remove high-leverage points. high-leverage points are those that are
outliers with respect to the independent variables. *Leverage points *are
those that cause large changes in the parameter estimates when they are
deleted.
Best,
Iraj
On Wed, Dec 7, 2011 at 10:16, John Bibby <[log in to unmask]>wrote:
> Dear Jim
>
> Your procedure is clearly not unbiassed. Consider for example if
> beta=0.999999
>
> Then your procedure is downwardly biassed.
>
> My earlier suggestion was designed to counteract this.
>
> Regards, JOHN
>
> On 7 December 2011 01:30, Jim Silverton <[log in to unmask]> wrote:
>
> > 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.
> >> >>
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> >> >
> >> >
> >> >
> >> > --
> >> >
> >> > 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.
> >> >
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> >
> >
> > --
> > Thanks,
> > Jim.
> >
> >
>
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