# Questions tagged [estimator]

For questions about estimators; an estimator is an approximations of a parameter that is using the avaiable data. There could be multiple estimators for a particular parameter.

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### Error term covariance of two-stage estimators

I am looking into properties of two-stage estimators (2SLS). My setting is as follows: 1) $y_1 = y_2\beta+\epsilon$ 2) $y_2 = z \pi_2 + \eta$. Equation 1 represents the second-stage estimation, ...
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### Finding the expectation of $\hat \theta$, if $\theta = \max(X_1, …, X_n)$ [duplicate]

I am trying to make $\hat \theta$ an unbiased estimator for a uniform distribution on $(0, \theta)$. So I am given the fact that $\hat \theta$ is the MLE for $\theta$, but I need to show that if I ...
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### Limit at $\theta \rightarrow 0$ is showing that $\frac{1}{n}\sum^n_{i=1}X^2_i$. is not the MLE?

Let $\mathbf X = (X_1, . . . , X_n)$ consist of independent and identically Normal $N(0, θ)$ random variables, with mean $0$ and variance $θ > 0.$ The density of $f_{\theta}(\mathbf x)$ is equal ...
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### How to show that this statistic is complete

Suppose that $S, {f_θ : θ ∈ Θ})$ is a statistical model, corresponding to an observed random vector $\mathbf X = (X_1, . . . , X_n).$ Let $\theta_1(\mathbf X)$ and $\theta_2(\mathbf X)$ be unbiased ...
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Suppose that $Y_1,...,Y_n$ is an IID sample from a uniform $U(\theta, 1)$ distribution. The method of moments estimator for $\theta$ is $\tilde \theta=2\bar Y-1$. The standard error of $\tilde \... 1answer 141 views ### If best unbiased estimator exists then it's maximum likelihood estimator? Our teacher proved in class that if the best unbiased estimator exists, then it is an MLE using a theorem that if$\hat{\theta}-\theta$is proportional to the score of$\theta$with probability$1$, ... 0answers 82 views ### Optimal unbiased estimator I have the sample$X_1,...,X_n$of i.i.d. from$U(\theta - 1/2; \theta +1/2)$. It is well known that$T = (X_{(1)}; X_{(n)})$is a sufficient but not complete statistic, because$X_{(n)}-X_{(1)} - (n-...
When the point estimator under consideration has a pdf , the $P[T=\tau(\theta)]=0$ , where $\tau(.)$ is some function of parameter $\theta$ and $T$ is an estimator of $\tau(\theta)$. But I did ...