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    $\begingroup$ Could you please clarify what you are asking? I do not see any "formulations" in your question--only formulas--so the meaning of "similar formulation to the least squares case" is not apparent. $\endgroup$ Commented Jan 20, 2014 at 16:30
  • $\begingroup$ My apologies. I meant formulation in the construction of a formula but did not mean anything more abstract. I have changed the the word to say "formula" rather than "formulation." $\endgroup$ Commented Jan 20, 2014 at 16:51
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    $\begingroup$ Note that your expression for $\hat{\beta}$ in the line starting with "The solution to..." is incorrect; you need to post-multiply by $y$. $\endgroup$ Commented Jan 20, 2014 at 21:47