# 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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### MVUE for a function of variance of Normal Distribution

Let $X_1, X_2, ..., X_n$ be a random sample from a $N(\theta_1,\theta_2)$ distribution. Find the uniformly minimum variance unbiased estimator of $3{\theta_2}^2$. Using factorization theorem, I found ...
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### Asymptotic Properties of OLS estimators

This is an econometrics exercise in which we were asked to show some properties of the estimators for the model $$Y=\beta_0+\beta_1X+U$$ where we were told to assume that $X$ and $U$ are independent. ...
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### 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 $1$, ...
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### What does symmetrised tuple mean?

I was reading the paper "Remarks on some nonparametric estimates of a density function" by Murray Rosenblatt (1956) and in one part he writes that an estimate $S(y;X_1,...,X_n)$ of the density ...
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### On the pooled variance in the estimating difference of means

Suppose that we need to compare means of two sample spaces, say P, Q. Let $\mu$ and $\nu$ be the expectation value of $P$ and $Q$, respectively. Consider $m$ independent random samples from $P$ and $n$...
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### Estimation of statistics of an iid sequence using Kalman filtering

I am given the sequence $v_0, v_1, \ldots$ of i.i.d. Gaussian random variables $\sim \mathcal{N}(\mu,\sigma^2)$ for some unknown parameter $\mu$ ($\sigma$ is known) which I need to estimate given the ...
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### Calculating Total Error In $g(x,y,z) = \frac{x-y}{z}$ Given Errors In Variables $x,y,z$

So I have a function given by: $$g(x,y,z) = \frac{x-y}{z}$$ where I can only estimate the values of $x,y,z$. I assume that these estimates are uncorrelated. From the Cramer-Rao lower bound, I know ...
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### Finding method of moment estimator from exponentially distributed random sample.

Given a random sample $X_1,...,X_n$ that are $IID$ from an exponential population with a unknown parameter $\lambda>0$ The parameter of interest is $\theta=\frac{1}{2}\sqrt{\lambda}$ Im looking ...
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### Unbiased estimator for $p^2$. Bernoulli distribution.

Let $X_{1},...,X_{n}$ be a random sample from Bernoulli (p), find an unbiased estimator for $p^{2}$. I think It's the same estimator for $\mathrm{Bin}(n,p)$ so: {V}(X) = np(1-p) = np - np^2 \\ p^2 ...
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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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### Bayesian estimator under 0-1 loss

If you were given the posterior distribution $P(\theta |X)$, as well as $P(X)$, and under no further assumptions, how could the Bayesian estimator be found under the 0-1 loss. I understand that I ...
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### Checking if estimator $\hat{\theta}=\frac{1}{n}\sum_{i=1}^{n}X_{i}^{2}$ is unbiased

Let $P_\theta(X=x) = \left(\frac{\theta}{2}\right)^2(1-\theta)^{1-x^2}$ for $x=-1,0,1$ Let $\hat{\theta}=\frac{1}{n}\sum_{i=1}^{n}X_{i}^{2}$ be an estimator of $\theta$. Is it unbiased? So the ...
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### Calculate the estimator and its standard deviation by Parametric Bootstrap

The third quantile of a distribution function F is the point q such that F(q) = 0.75. Note the q (α; λ) (Gamma distribution). Then, the quantile would be estimated by ^q = q (^α; ^λ). We do ...
### 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 ...
### How to show the first order condition of LAD estimator fo median regression is of order $o_{p}(\frac{1}{\sqrt{n}})$?
Given the model $y_{i}=x_{i}^{\prime}\beta_{0}+\epsilon_{i}$ with $E[sgn(\epsilon_{i})|x_{i}]=0$ and $E[sgn(\epsilon_{i}-c)|x_{i}] \neq 0$ if $c=c(x_{i}) \neq 0$, where \$sgn(\epsilon)=1-2 \cdot 1(\...