# 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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### MLE of Uniform on $(\theta, \theta +1)$ and consistency/bias

I see there were a few questions on SE about MLE of Uniform already but none of them helped me with this one: We are to compute MLE of $U(\theta, \theta +1)$ and check if it is biased and consistent. ...
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### Unbiased estimator questions

If $X_1,X_2,\ldots,X_n$ are i.i.d. $\mathrm{B}(1,p)$, find the best unbiased estimator of $p^n$. Attempt: Use indicator functions to show every observation has mean equal to 1 so this is the same as ...
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### Unbiased estimator of variance

My question is why is the best and most commonly used estimator for the variance (in a Gaussian distribution) the sample variance with constant 1/n-1 when the sample variance with constant 1/n+1 ...
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### Finding unbiased point estimate of population variance

Q.The contents of each of a random sample of 100 cans of a soft drink are measured. The results have a mean of 331.28 ml and a standard deviation of 2.97 ml. Show that an unbiased estimate of the ...
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### Estimator problems

I am stuck with some parts of a problem in my textbook, and the solutions in my textbook do not seem to help me. The problem goes: Two independent observations $X_1$ and $X_2$ are made of continuous ...
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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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### PDF of unbiased estimator

Given two samples $\left\{x, x\right\}$ which are independently observed from a $\mathcal{N}(0, \sigma^2)$ distribution. The estimator, $$\hat{\sigma^2} = \frac{1}{2}(x^2 + x^2)$$ is ...
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### Determine all $\overrightarrow{a}$ for which the estimator is an unbiased estimator for the variance

consider a random variable $X$ and stochastically independent repetitions $X_1,...,X_n$ of $X$. For each vector $\overrightarrow{a}=(a_1,...,a_n) \in \mathbb{R}^{n} \text{ with } a_i > 0$ we ...
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### Can L1 Distance Give Underestimates In a 2-D Rectangular Lattice?

I am working on this program that plays PacMan and involves calculating the Manhattan distance between the player and some enemies. Here's my problem, if we have an enemy straight ahead of the ...
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### Find the MoM estimator of $\theta$ when $X_i \sim N(a_i\theta, 1)$

Let $X_1, ..., X_n$ be independent random variables on some probability space such that for each $i = 1, ..., n$ we have that $X_i \sim N(a_i\theta, 1)$, where $a_1,...,a_n$ are given constants ....