A particular type of random coefficient regression

Hi all,

I have the model of type Y_i=Beta_0_i+Beta_1_i*X1_i+...+Beta_k_i*X_k_i, for i=1:n

There is no error term in this model, but for each person the betas are from a multivariate distribution.

I am ultimately interested in estimating the vector of mean for betas. If we rearrange betas around their mean we will get a heteroscedastic regression model oof the type


with B being the mean vector and M the covariance matrix of beta. OLS is an unbiased estimator here. But I guess more efficient estimators can be found as the variance has a known functional form.

Help is appreciated,