Paul, the factored likelihood method of Anderson easily yields the asymptotic covariance matrix of the transformed parameters of marginal of Y and regression of X on Y. The parameters of Y on X are functions of these parameters and can be computed using the delta method.
An even simpler way of getting standard errors is to simulate draws from the Bayesian posterior distribution of the factored likelihood parameters, and hence get draws of functions of these parameters. I would argue that inferences based on these draws are actually superior since they fully reflect uncertainty in the variance estimates. One source of these ideas is the Little and Rubin (2002) book, second edition. Rod Rod Little Richard D. Remington Distinguished University Professor Department of Biostatistics University of Michigan M4071 SPH II, 1415 Washington Heights Ann Arbor MI 48109 [email protected] On Wed, May 28, 2014 at 6:51 PM, Paul von Hippel < [email protected]> wrote: > Consider the classic situation where (X,Y) are bivariate normal with Y > complete and X incomplete. We wish to estimate the linear regression of Y > on X. There is a closed-form solution for the regression parameters, first > given by Anderson (1957). Is there also a known closed-form solution for > the asymptotic standard errors of the regression parameters? I see how the > standard errors could be obtained using the delta method, but I'm wondering > if someone has already done the legwork. > > Best wishes, > Paul von Hippel > LBJ School of Public Affairs > Sid Richardson Hall 3.251 > University of Texas, Austin > 2315 Red River, Box Y > Austin, TX 78712 > (512) 537-8112 >
