All Questions
12 questions
1
vote
1
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43
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Unbiased Variance MLE Distribution
If you take $10000$ samples from a normal distribution, the unbiased variance MLE (with Bessel's correction) is
$$\hat{\sigma}^2 = \frac{1}{9999}\sum_i (x_i - \hat{\mu})$$
Apparently the distribution ...
- 503
6
votes
1
answer
245
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Variance of MLE's in mixture distribution
I am studying mixture models, and I am interested in calculating the variance of the estimators using maximum likelihood. How is the variance calculated in this case? I already implemented the EM ...
- 281
1
vote
0
answers
103
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Adjusting standard errors in two-step maximum likelihood estimation
Suppose we want to solve
$$max_{\theta} \sum_{i}^N log f(y_i|x_i; \theta, \gamma).$$
Here, $\theta$ and $\gamma$ are two parameter vectors. The problem above derives an estimate of $\theta$, taking ...
- 21
1
vote
0
answers
36
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maximum likelihood estimation of the variance [closed]
In what situations the maximum likelihood estimation of the variance of distribution can severely ruin the estimation?
- 149
5
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2
answers
94
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What estimation method establishes sample mean and sample variance as estimators of mean and variance?
Sample mean and sample variance can be derived as MLE estimators for the mean and variance of a normal distribution.
For a distribution in general, what kind of estimation method leads to sample ...
- 19.8k
4
votes
1
answer
577
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Variance of MLE of a function of bernoulli parameter
Given $m$ i.i.d. Bernoulli( $\theta$ ) r.v.s $X_{1}, X_{2}, \ldots, X_{m},$ I'm interested in finding the variance (Not asymptotic) of estimator of $(1-\theta)^{1 / k},$ when $k$ is a positive ...
- 224
1
vote
1
answer
2k
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Estimation of the variance of MLE with small sample size and binomial distribution
Let $x$ be an observation from $X\sim Bin(n,p)$. I want to estimate $p$ and use ML estimator, $\widehat{p}=\frac{x}{n}$. I also want to estimate the variance of the estimator $\widehat{p}$. It equals: ...
- 441
15
votes
2
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376
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For what models does the bias of MLE fall faster than the variance?
Let $\hat\theta$ be a maximum likelihood estimate of a true parameter $\theta^*$ of some model. As the number of data points $n$ increases, the error $\lVert\hat\theta-\theta^*\rVert$ typically ...
- 363
0
votes
1
answer
385
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Mean of Sum vs Sum of Means with Maximum Likelihood estimation
The sum of the means of two normally distributed random variables is the same as taking the mean of the sum of the two signals.
Does this hold true for maximum likelihood estimation?
Is summing the ...
- 101
0
votes
0
answers
539
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Gaussian QMLE in estimating CCC-GARCH model
I am having some troubles understanding the estimation of a CCC-GARCH model (where the univariate GARCH models are GJR-GARCH(1,1)) by the means of Gaussian QMLE with the likelihood function of ...
- 173
3
votes
1
answer
8k
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Variance of the $\hat{\sigma}^2$ of a Maximum Likelihood estimator
Given some normally distributed observations $x_1,x_2,...,x_n$
$\forall i\ x_i\sim\mathcal{N}(\mu, \sigma^2)$
the ML estimator decides that the variance that maximizes the likelihood function is (see ...
- 271
5
votes
1
answer
422
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Conceptual question on estimation : How to calculate the variance of estimation error
EDIT/ UPDATE:
I have understood CRLB & why we need it. But my problem is something else. In book ...
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