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 May 1 awarded Informed May 1 accepted Gorgeous diophantine equation Apr 21 comment Gorgeous diophantine equation I found this problem in the ancient unnamed academic tutorial about the number theory. And I can't let go... Apr 21 asked Gorgeous diophantine equation Mar 2 revised What problems are related with the following type of FDE with delay? deleted 77 characters in body; edited title Mar 2 revised What problems are related with the following type of FDE with delay? added 266 characters in body Mar 2 revised What problems are related with the following type of FDE with delay? added 266 characters in body Mar 1 awarded Benefactor Mar 1 accepted The $\alpha$ estimation for the model $x_i = \xi_i \cdot \alpha$ Mar 1 revised What problems are related with the following type of FDE with delay? Clarifying Feb 26 revised What problems are related with the following type of FDE with delay? added 11 characters in body Feb 26 asked What problems are related with the following type of FDE with delay? Feb 25 revised The $\alpha$ estimation for the model $x_i = \xi_i \cdot \alpha$ clarifying Feb 25 comment The $\alpha$ estimation for the model $x_i = \xi_i \cdot \alpha$ I'm a little confused by the variance formula. Actually, we don't know the true $\alpha$. Can we substitute $\alpha^*$ by the its estimated value? Feb 24 comment The $\alpha$ estimation for the model $x_i = \xi_i \cdot \alpha$ Alexander, it's very good extension, thanks. The 3rd estimator is little bit surprising and at first sight it is unbiased. Could you specify the variance for it? Feb 22 comment The $\alpha$ estimation for the model $x_i = \xi_i \cdot \alpha$ Alexander, what about the reliability of the suggested estimate? Is it unbiased? What is the variance? Feb 22 revised The $\alpha$ estimation for the model $x_i = \xi_i \cdot \alpha$ deleted 2 characters in body Feb 22 awarded Promoter Feb 22 comment The $\alpha$ estimation for the model $x_i = \xi_i \cdot \alpha$ It's hard to believe thar PDF of $\epsilon_i(\hat \alpha)=(x_i \frac{\sum_i x_i/\delta_i}{\sum_i x_i^2/\delta_i} - 1)/\delta_i$ is most similar to $N(0,1)$. The goal of your solution is to minimize the variance of $\epsilon_i$ rather than to make it equal to 1. Furthermore, you don't take into account the mean of $\epsilon_i(\alpha)$ which should be close to zero. Feb 22 comment The $\alpha$ estimation for the model $x_i = \xi_i \cdot \alpha$ I think that a good estimation of $\alpha$ shoud make PDF of $\epsilon_i$ most similar to $N(0,1)$.