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Here, we assume that $\theta$ is an unknown parameter to be estimated. For example, $\theta$ might be the expected value of a random variable, $\theta=EX$. The important assumption here is that $\theta$ is a fixed (non-random) quantity. To estimate $\theta$, we need to collect some data. Specifically, we get a random sample $X_1$, $X_2$, $X_3$, $...$, $X_n$ such that $X_i$'s have the same distribution as $X$. To estimate $\theta$, we define a point estimator $\hat{\Theta}$ that is a function of the random sample, i.e.,

\begin{align}%\label{} \hat{\Theta}=h(X_1,X_2,\cdots,X_n). \end{align} For example, if $\theta=EX$, we may choose $\hat{\Theta}$ to be the sample mean \begin{align}%\label{} \hat{\Theta}=\overline{X}=\frac{X_1+X_2+...+X_n}{n}. \end{align}

There are infinitely many possible estimators for $\theta$, so how can we make sure that we have chosen a good estimator? How do we compare different possible estimators? To do this, we provide a list of some desirable properties that we would like our estimators to have. Intuitively, we know that a good estimator should be able to give us values that are "close" to the real value of $\theta$. To make this notion more precise we provide some definitions.

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