Handling missing attributes when using weighted average

I was trying this optimization where I have some predictors and I want to predict the real value using weighted average of the predictors. What I am trying to do is given the predictors' prediction and the ground truth values, I will calculate the weighted average and the weighted average has weights defined k1,k2,...kN for the N predictors such that when I take the weighted average the variance of the error of the weighted average is minimized.

Now at times, the predictors' predictions are missing. How can I handle these missing values?

If one of your predictions are missing, I'm guessing that the reason for that is that at least one of your predictor values (X) is missing for that observation.

If you want a prediction for that observation, you will have to supply the predictor variables that are missing. Ideally, you would take another measurement of the missing X variables. If that is impossible, you can impute the missing predictor values with k Nearest Neighbor analysis, an EM algorithm, or most crudely just the mean of the other predictors.