Logistic Regression | Exercise

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I am trying to solve questions 2 to 7 of this exercise exercise sheet

At the moment, I don't know how to answer these questions.

But I have some ideas for the second question :

  • Do I have to study this application ?

\begin{align*} R^{d} &\to R^{d}\\ y &\mapsto H_{n}(y)^{-1}\nabla ln(\beta^{*}). \end{align*}

  • A friend pointed out to me that question 2 may refer to Newton's method. That is to say that a step of Newton's method makes it possible to approach the solution. What do you think ?