All Questions
Tagged with estimators variance
94
questions
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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{\...
- 21
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0
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49
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Standard practice to show Biased CRBs
I have a problem with four-parameter estimation. I have derived the variances for the estimated parameters using Monte Carlo simulations (numerical ones) and theoretical ones using the inverse of the ...
- 235
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1
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What is the distribution of the unbiased estimator of variance for normally distributed variables?
I must be making some mistake in my derivation of the distribution of the unbiased variance estimator for i.i.d. $X_{i} \sim \mathcal{N}\left(\mu, \sigma^{2}\right)$.
We have $\bar{X} =\frac{1}{n}\sum\...
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82
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What is the variance decomposition method?
For $i = 1, \ldots, m$ and $j = 1, \ldots , n$ we have observations $x_{ij}$. We can assume that
$$
x_{ij} = y_{i} + z_{ij}, \qquad y_{i} \sim \mathcal{N}(\mu_{y},\sigma_{y}^{2}), \quad z_{ij} \sim \...
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Finding the Variance of the MLE Variance of a Joint Normal Distribution
I have a random sampling of $Z_1,...Z_n$ from a normal distribution $N(\mu,\sigma^{2})$. I am considering them within a joint likelihood function.
I know that the MLE ($\hat\sigma^{2}$) of $\sigma^{2}$...
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41
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Hierarchical models: Estimating variance and combining two estimators
Assume that $y_i \sim N(50,10)$.
I observe a signal with additive Gaussian noise $s_i \sim N(y_i, \sigma_d^2)$
I observe $n$ such signals, each corresponding to a different $y_i$.
I want to estimate $\...
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0
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29
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Reduce Variance of monte carlo estimator using guess of mean
Suppose you have a random variable $X$ and black-box function $f$. Suppose you also have prior estimates $m$ and $s$ of the mean and standard deviation of $f(X)$.
How can we use this prior information ...
- 111
3
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51
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Estimation Error Calculation
I'm learning about variance reduction for Monte Carlo methods and I am confused about how to calculate the "estimation error" of a given method.
My question is how should I interpret "...
- 133
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50
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Minimizing variance of sequence of independent but not identically distributed random variable
I tried to work on the problem
Let $(X_n)$ be a sequence of independent random variables with $E[X_n]=\mu$ and $Var[X_n]=n$ for every $n \in \mathbb{N}$. Find the statistic of the form $\sum_{i=1}^...
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Philosophical insight of Bias Variance Decomposition
As we know that we can perform a Bias Variance decomposition of an Estimator with MSE as loss function and it will look like below:
$$\operatorname{MSE}(\hat{\theta}) = \operatorname{tr}(\operatorname{...
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3
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941
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Variance estimation for small sample size
The following variance estimator of a set of data points $x = (x_1, ..., x_N)$
$$
\text{Var}\,(x) = \frac{1}{N-1} \sum_{i=1}^N (x_i - \bar{x})^2
$$
has itself a large variance when $N$ is small (in my ...
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1
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76
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Is $\sum(x^2 - \bar{x}^2)/(n-1)$ an unbiased estimator of variance?
We know that sample variance $\sum(x- \bar{x})^2/(n-1) = \sum(x^2- 2x\bar{x}+\bar{x}^2)/(n-1)$ is an unbiasedd estimator of variance
Is $\sum(x^2 - \bar{x}^2)/(n-1)$ also an unbiased estimator of ...
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What is the expression for covariance in the context of Monte-Carlo estimator? [duplicate]
I am trying to calculate the variance:
$$
\langle(\bar{O}-<O>)^2\rangle
$$
of the Monte-Carlo estimator
$$
\bar{O}=\frac{1}{M}\sum_{m=1}^M{O_m}
$$
For uncorrelated samples.
In order to do so, I ...
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37
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Variance of an estimator [duplicate]
I have tried to proof the variance of this estimator.
Is this right?
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35
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Bias and variance of estimators - Normal Sample
If we consider the two following estimators $$\hat{\mu_1} = \frac{\bar{X_1}+\bar{X_2}}{2}$$ $$\hat{\mu_2} = \frac{n_1\bar{X_1}+n_2\bar{X_2}}{n_1+n_2}$$ where $X_1, X_2$ are samples from a normal ...
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