All Questions
Tagged with estimators maximum-likelihood
111
questions
2
votes
0
answers
46
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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 ...
4
votes
2
answers
124
views
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 ...
- 250
1
vote
1
answer
34
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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 ...
- 383
0
votes
0
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18
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Demonstrating $SU=U(\sigma^2 I+D^2)$ as a Sufficient Condition in Maximum Likelihood Estimation
I am working on an exercise related to maximum likelihood estimation (in the context of principal component analysis) for the distribution
$$p(x) = Gauss(b, WW^T+\sigma^2I)$$
In particular, I want to ...
- 153
5
votes
2
answers
128
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Sufficient conditions for asymptotic efficiency of MLE
Maximum-likelihood estimators are, according to Wikipedia, asymptotically efficient, that is they achieve the Cramér-Rao bound when sample size tends to infinity. But this seems to require some ...
- 1,099
2
votes
1
answer
86
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Maximum Likelihood Estimation for a Unique Probability Density Function
In the context of estimating parameters for a uniquely distributed set of independent and identically distributed random variables, I am examining the following probability density function $ f(x|\...
- 425
1
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0
answers
33
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Large samples property of bayes procedures
I was reading through Wasserman's All of Statistics and I came across this property in the Bayesian statistics chapter:
I think I don't really get what is supposed to be the intuition behind it, and ...
- 41
0
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0
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29
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How to derive the (partial) maximum likelihood estimator for a simple autoregressive model
I am trying to derive two maximum likelihood estimators which I have seen in a statistics book, but I am unable to derive them and would really like some help.
It goes like this:
Consider the simple ...
- 65
1
vote
1
answer
69
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Does increasing number of observations lead to the decreasing of Mean Square Error of consistent estimators?
I know that not all weakly consistent estimators exhibit MSE-consistency : https://stats.stackexchange.com/a/610835/397467.
Anyway, does increasing the sample size leads to a reduction in their mean ...
- 11
1
vote
1
answer
78
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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 $\sigma^{2}$...
- 13
0
votes
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answers
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 $\...
- 1
1
vote
2
answers
207
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Bayesian Learning: Finding the variance of noise
Suppose $x_i \sim N(10,4)$ - ie, the distribution is known.
There is a noisy signal $s_i \sim N(x_i, \sigma_e^2)$ and I want to estimate $\sigma_e$.
I see some pairs ($s_i, x_i$) but they are not '...
- 23
1
vote
1
answer
32
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Generating "surrogate data" to calculate error on estimators
We have a dataset in the form of a time series $Y_n$.
We assume it follows an underlying parametric distribution $f(n,\beta)$, $\beta$ being the parameters.
From the observed dataset, we get an ...
- 113
0
votes
1
answer
539
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Maximum-likelihood estimator for data points with errors
Suppose there are N measurements of a random variable x which has Gaussian p.d.f. with unknown mean $\mu$ and variance $\sigma^2$. Classical textbook solution for estimation $\mu$ and $\sigma$ is to ...
2
votes
2
answers
682
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What does the likelihood function converge to when sample size is infinite?
Let $\mathcal{L}(\theta\mid x_1,\ldots,x_n)$ be the likelihood function of parameters $\theta$ given i.i.d. samples $x_i$ with $i=1,\ldots,n$.
I know that under some regularity conditions the $\theta$ ...
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