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In this lecture on method of moment, we have:

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enter image description here why is gradient of psi inverse a dxd matrix? K-th moment $m_k$is defined as $ \mathbb E[X^k] $ and can be estimated by the average using Law of Large Numbers which here is represented by $\hat m_k$ My understanding is that the inverse function $\psi^-1 $ takes the vector of moments of size d, so why isn't the gradient of size d?

Mina
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    Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures. – José Carlos Santos Nov 23 '20 at 07:29
  • Your question is cryptic. You should explain what the moments (with an "s" are, with repect to which they are taken etc. – Jean Marie Nov 23 '20 at 08:20
  • @JoséCarlosSantos oh what a life saver thanks for the tip. I incorporated it. – Mina Nov 23 '20 at 15:21
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    @JeanMarie I added the definition of moments in statistics. Is that now more clear? Thank you so much for providing feedback on this. – Mina Nov 23 '20 at 15:22

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I have found the answer. Normally, for a function $\psi$ that goes from $\mathbb R^d$ to $\mathbb R$ then you have to take the derivative of the function in regards to each of the d parameters and you will have a vector of size d. In this case $\psi$ is a function from $\mathbb R^d$ to $\mathbb R^d$ therefore you will end up with a d-dimensional array for each of d elements in the "y" side.

Mina
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