a question regarding statistics

[Ahmad]

i have found this explanation so far can you please guide me if you understand what the author has done??

"The t-statistics associated with the mean coefficients in Table 2 have been adjusted for cross-equation correlations. We extend the correction in standard errors proposed in Chordia et al. (2000) by allowing the variance and pairwise covariances between coefficient estimates to vary across securities. The variance of each estimated coefficientβ_i is obtained from stock i’s liquidity-return regression in (2). The empirical correlation between the regression residuals for stocks i and j is used to estimate the pairwise correlation between the coefficients{β_i andβ_j }. Hence, the standard error of the mean estimated coefficient is ...

please find the attached JPEG file it is just snapshot of the equation used, dont know how to enter an equation here. thanks

[SteveDenham]

The equation given is a pretty standard summation version of the standard error of a difference between two correlated variables.  Plug in the necessary variables, get the std error, and calculate the t value as the difference between the estimates divided by the standard error.

Steve Denham

[Ahmad]

thanks , but the problem is i have hundreds of b's which are the necessary variables. they sat that they have calculated the pairwise correlation from the rsu=iduals of the orignal regressions, so how to calculate the pairwise correlation of  residuals of these 100 equations???

[SteveDenham]

A possibility is to extend 's idea of a shift to GLM even farther to use MIXED.  The following is untested, but might work:

ods output corrb=corrb solutionf=solutionf;

proc mixed;

class stockName;

model liq = stockName x z d / solution noint corrb;

run;

The corrb option should give the pairwise correlations you need (there may need to be some nesting to get stuff right, but for now try this).  The regression coefficients should be in the solutionf dataset.

Steve Denham

Message was edited by: Steve Denham

[Ahmad]

and here is the other paper, to which the author of the previous paper is referring to

[PGStats]

Maybe all you need is some descriptive statistics for a population of 500 regression parameters. Maybe, you could do something simple as in the folowing example:

proc sort data=sashelp.cars out=cars; by origin; run;

proc reg data=cars outest=carsEst noprint;
by origin;
model horsepower = engineSize Weight;
run;

proc summary data=carsEst noprint;
var engineSize Weight;
output out=carsMeanEst mean= std= probt= / autoname autolabel;
run;

proc print data=carsMeanEst; run;

PG

PS. Just don't associate my name to that idea!  - PG