Ricardo,
I am not sure. Papers I have read that use this transformation refer to:
Burbidge, John B., Lonnie Magee, and A. Leslie Robb, 1988 "Alternative Transformations
Handle Extreme Values of the Dependent Variable" Journal of the American
Statistical Association, 83(401).
but I do not have access to this journal, so I am not sure how the optimal theta is
derived.
However, as z becomes large, ln(theta*z + sqrt(theta^2 * z^2 +1 )) is approximately
equal to ln(2*theta) + ln(z), which a simply a shift in the logarithm
(Pence, Karen M., "401(k)s and Household Saving: New Evidence from the Survey of
Consumer Finances," FEDS Working Paper 2002-06, January 2002.
http://www.federalreserve.gov/pubs/feds/2002/200206/200206pap.pdf ).
Scott
----- Original Message -----
From: Ricardo Ovaldia <[email protected]>
Date: Thursday, March 31, 2005 11:22 am
Subject: Re: st: Inverse hyperbolic sine function
> --- [email protected] wrote:
> > 1. Yes, but more generally, the ihs fuctions is
> > ln(theta*z + sqrt((theta^2 * z^2
> > + 1))/theta; where theta is scale parameter that
> > could be estimated.
>
> Is IHS = log(z + sqrt(z^2 + 1)) then only an
> approximation? If so, I assume that it is good when z
> is large relative to 1/theta. But how can we know
> ahead of time how good the approximation will be on
> our data?
>
> Regards,
> Ricardo.
>
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