Questions tagged [estimators]
A rule for calculating an estimate of a given quantity based on observed data [Wikipedia].
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confidence intervals for proportions containing a theoretically impossible value (zero)
This is really a hypothetical question not related to an actual issue I have, so this question is just out of curiosity. I'm aware of this other related question What should I do when a confidence ...
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No Existence of Efficient estimator
I need to prove that given $(X_1,...,X_n)$ from the density $$\frac{1}{\theta}x^{\frac{1}{\theta}-1}1_{(0,1)}$$ no efficient estimator exists for $g(\theta)$=$\frac{1}{{\theta}+1}$.
I have shown that ...
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Unbiased Estimator of Nugget Effect
Question: I am trying the measure the nugget effect, which is parameterized by $(1-\lambda)$ in the following variance-covariance used to describe the multivariate normal distribution of my n-...
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How to accurately estimate the probability of a rare event in a large dataset?
I have a dataset of 30,155 names and out of curiosity I verified that the longest name has 68 characters, which is quite big considering the mean and SD were 24.78 and 5.64, respectively. Based on ...
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Calculating the mean and error for correlated measurements involving different estimators and quantiles
My goal is to find a way to report a mean $\pm$ error for different estimators and quantiles of the same distribution (same measurement).
I am measuring the width of a distribution (Gaussian core and ...
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Unbiased and consistent estimator with positive sampling variance as n approaches infinity? (Aronow & Miller) [duplicate]
In Aronow & Miller, "Foundations of Agnostic Statistics", the authors write on p105:
[A]lthough unbiased estimators are not necessarily consistent, any unbiased estimator $\widehat{\...
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Maximum liklihood estimators for simple linear regression with $\sigma^2$ unknown
Suppose that we have the simple linear regression model for the form:
$$Y_i = \beta X_i +\varepsilon_i$$
With the following set of 'classical assumptions' holding:
$E(\varepsilon_i)=0$
$Var(\...
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Sum of asymptotically independent random variables - Convergence
Let $\theta_N=\frac{1}{N}\sum_{i=1}^N \pi_i\cdot g_i$ where $0<\pi_i<1$ and $0<g_i<1/\pi_i$ such that $\theta_N\overset{N\rightarrow \infty}{\rightarrow}\theta$.
If $X_i\sim Ber(\pi_i)$, I ...
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Must maximum likelihood method be applied on a simple random sample or on a realisation?
I guess my trouble is not a big one but here it is: when one applies maximum likelihood, he considers the realization $(x_1, \dots, x_n)$ of a simple random sample (SRS), leading to ML Estimates. But ...
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Asymptotic unbiasedness + asymptotic zero variance = consistency?
Here, Ben shows that an unbiased estimator $\hat\theta$ of a parameter $\theta$ that has an asymptotic variance of zero converges in probability to $\theta$. That is, $\hat\theta$ is a consistent ...
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Is Coefficient of Variation a valid measure of relative efficiency?
I'm wondering if it is always valid to use Coefficient of Variation (CV) to determine relative efficiency of parameter estimators, and to compute statistically equivalent sample sizes based on that ...
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Using Rao-Blackwell to improve the estimator of P(X/Y < t)
X and Y are independent N (0, 1) random variables, we want to approximate P (X/Y ≤ t), for a fixed number t.
The first part of the problem was to describe a naive Monte Carlo estimate. I described ...
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What is the difference between unbiasedness, consistency and efficiency of estimators? How are these interrelated among themselves? [duplicate]
!Efficiency(https://stackoverflow.com/20240427_193105.jpg). Given snapshot of the book states that among the class of consistent estimators, in general, more than one consistent estimator of a ...
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Terminology clarification about sample moments
According to MathWorld (link): "The sample raw moments are unbiased estimators of the population raw moments".
While in Wikipedia (link) it is said:
...the $k$-th raw moment of a population ...
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Why can we get better asymptotic global estimators even for IID random variables?
Let $X_1,...,X_N$ be IID random variables sampled from a parametrised distribution $p_\theta$, and suppose my goal is to retrieve $\theta$ from these samples.
We know that the MLE provides an ...
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