# Questions tagged [estimators]

A rule for calculating an estimate of a given quantity based on observed data [Wikipedia].

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### Method of moments estimator, $P_\theta(X = x) = \frac{1}{\theta}$

I am struggling with finding a method of moments estimator for (seemingly) simple situation: pdf is given by $P_\theta(X = x) = \frac{1}{\theta}$, $x \in$ {1,2,...$\theta$}, where $\theta \in N$. My ...
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### Bias-Variance Trade Off with Cauchy Estimator

I'm having a look at the bias and standard error of a set of estimators. I expected to see the trade off when varying the parameter of the estimator, but I see that both the bias and the variance ...
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### Is $\hat{\sigma^2}=\hat{\sigma}^2$?

In simple linear regression $$Y_i=b_0+b_1X_i+\varepsilon_i$$ where $$\varepsilon_i\sim N(0, \sigma^2)$$ is it true to say that the estimator for variance and the estimator for SD squared are equal? I ...
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### More efficient estimator in this situation?

I am thinking about the following situation (it is an example): There are N families in a city and we have a simple random sample of size n. In that sample we know that there are $x_{0}$ families with ...
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### Estimate mean of Poisson from binary data

If you assume that counts in sample units would be distributed according to a Poisson distribution, but the data that you have are observations of only presence (count would be 1 or more) or absence (...
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### Expectation of Sample Variance

This is a question from the book Casella and Berger: where $ES$ actually means $\mathbb{E}(S)$ (expectation of S) So, I manage to use the Jensen Inequality to prove that $\mathbb{E}(S) \leq \sigma$,...
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### Show that a linear combination of UMVU estimators is also a UMVU estimator

Suppose I have two estimators $\delta_1$ and $\delta_2$ with finite second moments, and they are UMVU estimators of $f_1(\theta)$ and $f_2(\theta)$, respectively. Now, for some real numbers $n_1$ and ...
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### Difference between “Within” estimator for $Y_\textit{diff} = Y_{t_i} - Y_{t_{i - 1}}$ vs “First Difference” estimator for $Y_{t_i}$

I am using a diff-in-diff strategy and have a few question. I am not getting equivalent coefficient estimates for the two following regressions on panel data: a panel regression with a fixed ...
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### Are a distribution's higher-order features harder to estimate?

In what sense, if any, are a distribution's higher-order features (e.g., moments, cumulants) harder to estimate than its lower-order features, for at least some distributional families? For example, ...
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### “Ice skater” / “figure skating” / “ISU” method of discarding outliers

So I need a way of ruling out outliers and "the ice skater method" has been suggested. The person who suggested it has a good deal of experience of doing the task I am doing, so I am certainly ...
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### How do I correctly estimate the size of a subpopulation using noisy observations?

To preface this question: please comment on whether my description of the problem is missing details or the problem itself is not well-posed as I'm seeing a lot of views but no activity. I am trying ...
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### What are the differences between HC estimators and their small sample properties?

I am currently using R to run regression with the following code: ...
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### “Magical” variance reduction problem

I recently came across this toy problem: You have two sticks of unknown lengths $a>b$ and a measuring device with constant variance $1$ that you can only use twice. How can you construct ...
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### Parameter estimation by averaging over all high-likelihood possibilities?

I am refereeing a chemistry paper. The authors are trying to interpret some experimental data by comparison with numerical simulations. They have run many simulations using different combinations of ...
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### Skewed outcome variable, sem model: is it a problem?

My outcome variable is really skewed, and I want to include it in a SEM model (I am using lavaan - R). It is measured with a 7-points Likert scale (agreement) and consists of 5 items. If the model ...
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### Minimax estimators in Bayesian analysis

I got recently introduced to minimax methods in statistical decision theory. Is there an analogue in Bayesian analysis and some resources related to this?
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### What may be an inefficient estimator of the population mean?

If the sample mean is an efficient estimator of the population mean, what may be an example of an inefficient such estimator?
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### quantifying asymmetry on a sphere

I have a scalar quantity that is distributed on a sphere. I would like to quantify the asymmetry in this scalar field. is there any standard method to do this? Let's say that the function on the ...
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### L1 distance between categorical distribution and any arbitrary estimator?

Given an unknown categorical distribution $p$ over $k$ categories, and any arbitrary estimator of this distribution vector $q$ constructed from $n$ i.i.d samples, can anyone point me to some results ...
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### Is sample mean square is a consistent estimator of population variance?

If x ~Normal with population mean u and population variance (sigma)^2 Then is sample mean square which is asymptotically unbiased estimator for population variance then is it also consistent ...
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### Proof for how the drift estimator, for a random walk with drift, is unbiased?

Random walk with drift formula is: (Yt = α + Yt-1 + εt ) How do I go about checking that the drift estimator α-hat is unbiased.. which is proving that E(α-hat) = α? Is this something I would need ...
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### variance estimator for a symmetrical two-sides censored normal distribution

Suppose to draw a sample of $n$ observations from $X \sim \mathcal{N}(0,\sigma)$, with observations outside the interval $(-c,+c)$ censored; $c$ is known and one can conveniently set $c=1$, for ...