Questions tagged [unbiased-estimator]
Refers to an estimator of a population parameter that "hits the true value" on average. That is, a function of the observed data $\hat{\theta}$ is an unbiased estimator of a parameter $\theta$ if $E(\hat{\theta}) = \theta$. The simplest example of an unbiased estimator is the sample mean as an estimator of the population mean.
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Unbiased estimator for 1/Var(X)
Suppose I have iid observations $(X_1, \dots, X_N)$. Is there an unbiased estimator for $1 / \text{Var}(X)$?
Clearly, we can't just take the reciprocal of an unbiased estimator for $\text{Var}(X)$; by ...
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Is the sample MSE an unbiased estimator of any quantity?
We assume that there is a true function $f$ such that $y_i = f(x_i) + \varepsilon_i$. In any general regression setting, a common measure of the quality of the estimated true function, $\hat{f}$, is ...
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Intuition of Bessel-like corrections for higher-order moments
Bessel's correction is understood as an adjustment to the sample variance that renders it an unbiased estimator of the population variance for an iid sample. This is generalized for higher central ...
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Minimizing MSE for the estimator of population variance
The screenshot below is from the Wikipedia page on Mean Squared Error. Can someone please either
help me understand the last highlighted sentence (given the claim is correct),
or confirm my suspicion ...
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Deriving unbiased estimator for standard deviation with gamma distribution
For some $X_1,...,X_n \sim N(\mu, \sigma^2)$ with both parameters unknown, I'm trying to derive the unbiased estimator for $\sigma$ from the MLE.
We know that the $\hat{\sigma} = \sqrt{\frac{1}{n}\...
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In NLLS, how do you produce accurate estimates of RMSE(true_params) given RMSE(global_minimum_params)?
I have an exponential decay
$f(t) = \sum_n \left( A_n e^{-\frac{t}{\tau_n}} \right) + c + \epsilon(t)$,
where n represents the different exponential decay components, $A_n$ represents each decay ...
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When is a maximum likelihood estimator biased? [duplicate]
It is known that maximum likelihood estimators (MLE) can be biased. Can we predict whether a given distribution and parameter of interest will produce a biased MLE? On what properties does it depend? ...
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Finding the variance of an unbiased estimator [duplicate]
I tried finding the Cramer Rao Lower Bound for Variance and got (λ/n)*exp(-2λ). Then I got stuck as the UMVUE doesn't coincide with the CRLB so can't exactly find the variance of exp(-λ), I only ...
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What is the point of unbiased estimators if the value of true parameter is needed to determine whether the statistic is unbiased or not?
The definition that I have for an unbiased estimator is: "A statistic used to estimate a parameter is an unbiased estimator if the mean of its sampling distribution is equal to the value of the ...
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Can the bias of an estimator depend on the number of observations? Practical interpretation of the expected value
Here it says that
$\hat{\theta}=\frac{1}{n} \sum x_i + \frac{1}{n}$
is a biased estimator of the sample mean.
Let's see:
\begin{align}
\mathbb{E}(\hat{\theta}) &= \frac{1}{n} \sum \mathbb{E}(x_i) +...
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Question about Unbiasedness of Raw Sample Moments, Odd Simulation Results
I'm performing a Monte Carlo simulation to confirm that $$m_k'=\frac{1}{n}\sum_{i=1}^n X_i^k$$ is an unbiased estimator for $\text{E}[X^k]$. In the event $X\overset{iid}{\sim} \chi_1^2$, we have $\...
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How to find a de-biased estimator with a ML component in my contaminated data problem?
I am trying to use the output of a machine learning model to estimate (using a maximum likelihood approach) a parameter in a distribution. The estimator I get has a bias which is much larger than the ...
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Calculating population estimators when number of units sampled in a stratum is $\leq$ 1
A survey of 100 houses across 20 states in a country is conducted with each state being used as a stratum. To find the population mean I know i need to use the formula
$$\bar{y}_{str}=\sum^{20}_{h=1} \...
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Is $\mathbb{E}\left[\|\hat{\Sigma}\|_F\right]=\|{\Sigma}\|_F$?
In one paper I read, the authors write
$$
\mathbb{E}\left[\|\tilde{\Sigma}^{-\frac{1}{2}}\left(\hat{\Theta}-\Omega\right)\|_F^2\right]=\mathbb{E}\left[\|{\Sigma}^{-\frac{1}{2}}\left(\hat{\Theta}-\...
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Underestimation of Empirical Coefficient of Variation When Sampling from a Log-Normal Distribution with High CV
I am working with a log-normal distribution where I input a coefficient of variation (CV) to generate the variance. I then sample 𝑛 times from this distribution. The issue I am encountering is that ...
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