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I am trying to do a GMM(Generalized Method of Moments) by NMinimize, it comes up with the warning 'The objective function is not a scalar', here's what I have tried:

  1. I adjusted the function step by step and found that the problem is about the minus e=y-y`Pred, after I delete the minus, it worked.But I really can't understand why.
  2. When I use the functions directly, it gives a scalar. I think this is the evidence that my dimension of vector and matrix is right, which I have checked also.

I am new with the matrix calculate, I think this problem must be somehow stupid, but I can't fix it.Sorry :(

ClearAll[data`x, data`y, Winv, params, gmmObjective, beta]

(*Setting*)
data`x = {{1, 2, 3}, {4, 5, 6}};

data`y = {1, 2};

Winv = IdentityMatrix[3];

(*Original function*)
gmmObjective[params_, y_, x_, Matr_] := 
 Module[{y`Pred, e, moments, avgMoment, ju`value},
  y`Pred = x . params;
  e = y - y`Pred;
  moments = e . x;
  ju`value = moments . Matr . Transpose[moments];
  Return[ju`value];
  ]

NMinimize[{gmmObjective[beta, data`y, data`x, Winv], 
  Element[beta, Vectors[3, Reals]]}, beta]


(*Adjusted function*)
gmmObjective[params_, y_, x_, Matr_] := 
 Module[{y`Pred, e, moments, avgMoment, ju`value},
  y`Pred = x . params;
  e = y`Pred;
  moments = e . x;
  ju`value = moments . Matr . Transpose[moments];
  Return[ju`value];
  ]

NMinimize[{gmmObjective[beta, data`y, data`x, Winv], 
  Element[beta, Vectors[3, Reals]]}, beta]
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    $\begingroup$ The porblem is with beta... try NMinimize[ gmmObjective[{beta1, beta2, beta3}, datay, datax, Winv], {beta1, beta2, beta3}] with your original objective and it gives an answer. $\endgroup$
    – bill s
    Nov 25, 2023 at 3:21

1 Answer 1

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You define beta in NMinimize as a scalar. Replacing beta by: 1 and evaluating:

gmmObjective[1, data`y, data`x, Winv]

{{1, 2, 3}, {4, 5, 6}} . 1 . {{1, 2, 3}, {4, 5, 6}} . 
 Transpose[{{1, 2, 3}, {4, 5, 6}} . 1 . {{1, 2, 3}, {4, 5, 6}}]

You see: "...6}}.1.{{1,2..." You can not use the Dot product for a scalar. Your statement:

y`Pred = x . params

is wrong.

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