Suppose I need to estimate a parameter matrix and one way is to write the derivation in matrix form and get the optimized matrix directly, the other way is the estimate each row of the matrix and then form the optimized matrix. I found these two methods didn't give the same results. what would be the possible reason?
What's the difference between two way to estimate a parameter matrix?
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matrices
estimation-theory
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0The joint optimization problem, that takes the entire matrix into account, should outperform the row-wise estimation. It is able to get the best result over the entire space. The row-wise estimation can only do the best it can with each row, then paste the results together. In essence, it has less degrees of freedom. Since the row-wise estimation would be a feasible solution to the matrix-wise estimation, we can say that the matrix-wise estimation should be better as it could consider all row-wise solutions....1/2 – 2017-01-30
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0...This is, of course, assuming you have a proper optimization problem being solved to global optimality. Since I don't know exactly what, or how, you're estimating, I can't state this with certainty. 2/2 – 2017-01-30