Math 6010 • Linear Models

Let \(Y_i=\alpha^{i/n}+\epsilon_i\), \(1\leq i\leq n\). We assume that \(\epsilon_1,\epsilon_2,\ldots,\epsilon_n\) are independent, identically distributed random variables with \(E\epsilon_i=0\), \(0<\sigma^2=\operatorname{var}\epsilon_i<\infty\) and \(E\epsilon_i^4<\infty\).
\begin{parts}
\item Find the least-squares estimator for \(\alpha\).
\item Show that the estimator is asymptotically normal.
\item Find an estimator for \(\sigma^2\).
\end{parts}