After debugging the LOD imputation procedure, I found that the algorithm can fail to converge when a very high percentage of the data is censored. In each case that I found, the estimated sigma parameters would go to infinity while the estimated nuggets would go to 0. This would continue until the algorithm crashed due to a numerically singular covariance matrix. I'm hoping that this was an artifact of the simulation parameters I was using and that it won't be an issue on real data. But I thought I should make a record of the fact that this problem exists. If we run into this issue later, I will experiment with ways to fix it.
After debugging the LOD imputation procedure, I found that the algorithm can fail to converge when a very high percentage of the data is censored. In each case that I found, the estimated sigma parameters would go to infinity while the estimated nuggets would go to 0. This would continue until the algorithm crashed due to a numerically singular covariance matrix. I'm hoping that this was an artifact of the simulation parameters I was using and that it won't be an issue on real data. But I thought I should make a record of the fact that this problem exists. If we run into this issue later, I will experiment with ways to fix it.