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standard error of the ratio of two covariance estimates
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Harry Garst
Feb 5, 2013, 7:38:09 AM2/5/13
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Is the sampling distribution of the ratio of two covariances estimates
known? I would like to estimate the standard error of this ratio. Any
help is welcome.
kind regards,
Harry
known? I would like to estimate the standard error of this ratio. Any
help is welcome.
kind regards,
Harry
Ray Koopman
Feb 5, 2013, 2:10:47 PM2/5/13
to
let alone its s.d.
Harry Garst
Feb 5, 2013, 5:14:26 PM2/5/13
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weight is estimated as cov(z,y1)/cov(z,y2). Could I use the standard
error of this regression coefficient?
Ray Koopman
Feb 5, 2013, 8:56:44 PM2/5/13
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On Feb 5, 2:14 pm, Harry Garst <harry.ga...@gmail.com> wrote:
> On Feb 5, 8:10 pm, Ray Koopman <koo...@sfu.ca> wrote:
because the density of the denominator is positive at zero.
If you're looking at a standard error given by some computer program
then check the manual to see how it has been obtained. I suspect you
have some sort of asymptotic approximation; e.g., Kendall & Stuart,
vol 1, sec 10.7, eq 10.17, p 232 in my 1963 ed.
> On Feb 5, 8:10 pm, Ray Koopman <koo...@sfu.ca> wrote:
>> On Feb 5, 4:38 am, Harry Garst <harry...@gmail.com> wrote:
>>
>>> Is the sampling distribution of the ratio of two covariances
>>> estimates known? I would like to estimate the standard error
>>> of this ratio. Any help is welcome.
>>>
>>> kind regards,
>>> Harry
>>
>> I've never seen one. In general, not even its mean would be
>> defined, let alone its s.d.
>
> In a bivariate instrumental variable regression model the regression
> weight is estimated as cov(z,y1)/cov(z,y2). Could I use the standard
> error of this regression coefficient?
Neither the mean nor the standard error of the ratio is defined,
>>
>>> Is the sampling distribution of the ratio of two covariances
>>> estimates known? I would like to estimate the standard error
>>> of this ratio. Any help is welcome.
>>>
>>> kind regards,
>>> Harry
>>
>> I've never seen one. In general, not even its mean would be
>> defined, let alone its s.d.
>
> In a bivariate instrumental variable regression model the regression
> weight is estimated as cov(z,y1)/cov(z,y2). Could I use the standard
> error of this regression coefficient?
because the density of the denominator is positive at zero.
If you're looking at a standard error given by some computer program
then check the manual to see how it has been obtained. I suspect you
have some sort of asymptotic approximation; e.g., Kendall & Stuart,
vol 1, sec 10.7, eq 10.17, p 232 in my 1963 ed.
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