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# Questions tagged [maximum-likelihood]

For questions that use the method of maximum likelihood for estimating the parameters of a statistical model with given data.

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### Likelihood of Bayes' theorem [closed]

When estimating the parameter (hypothesis), I thought it was correct to compare the values of "P(hypothesis_i | observed data)" by changing i for each hypothesis However, when applying Bayes'...
0 votes
1 answer
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### Question about likelhood function of discriminative models

Im a little confused with the likelihood function. For discriminative models, we have a hypothesis function $h_{\theta}(x) = p(y \mid x ; \theta)$. Using the principles of maximim likelihood we want ...
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### Trigamma-free Negative Binomial regression: doubts on Hessian and Fisher Information Matrix in the dispersion parameter

I have been looking at alternative versions of the Hessian and Fisher (expected) Information Matrix for the Negative Binomial regression specification, which are given by widely-cited academic sources ...
• 63
4 votes
3 answers
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### Maximum Likelihood Estimation for Poisson Mean with Given Observations

You have a sample of $n$ i.i.d. realizations of the random variable $X$ distributed as a Poisson with parameter $\lambda$. It is known that: $n_1$ values are greater than or equal to $2$; $n_2$ ...
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1 vote
1 answer
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• 3,318
2 votes
1 answer
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### Efficient and unbiased estimation of the location ($\mu$) of truncated normal distribution with known scale ($\sigma^2$) and truncation points

I have one observation $x$ which I know comes from the following truncated normal distribution: $$x \sim TN(\mu, \sigma^2, -\delta, \delta) \;\textrm{ where }\; \delta > 0$$ In my problem, the ...
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4 votes
2 answers
257 views

2 votes
1 answer
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• 113
0 votes
0 answers
59 views

0 votes
0 answers
11 views

### Logit panel with Simulated Maximum Likelihood

I'm testing a very basic logit panel model in matlab. The setup is as follows: We observe a binary variable $y_{it} = 1(\beta_0 + \beta_{it}x_{it} + \varepsilon_{it} > 0)$ where i is individual and ...
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1 vote
1 answer
59 views

• 113
1 vote
1 answer
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4 votes
1 answer
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### Maximizing log-likelihood: Determinining whether critical points are maximums

Consider the following proof of the fact that $\bar{X}$, the sample mean, is the MLE of parameter $\lambda$ in a Poisson distribution. Let $x_1, \ldots, x_n$ be the observations of $X_1, \ldots, X_n$ ...
• 3,468
0 votes
0 answers
44 views

### What does singular hessian in optimization tell me

I am doing optimization using maximum likelihood estimation, and when I am trying to get the standard errors of estimates using hessian matrix, I get non-invertible/singular hessian warning. After I ...
• 123
0 votes
0 answers
21 views

### Deriving MLE & asymptotic variance manually - for which distributions/cases is it possible?

I am interested whether you know any distributions or special cases where the maximum likelihood estimator, the theoretical and estimated asymptotic variance can be fully derived manually, i.e. which ...