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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EM Algorithm for Missing Data in Multivariate Data [closed]

I am currently trying to understand the EM algorithm and solve the following problem: I have a dataset with 10 different variables in which there can be missing values. The problem is that I think the ...
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Show that $\log |\Sigma|+\text{Tr}(\Sigma^{-1}V)$ is uniquely minimized

Let $V$ be an $n\times n$ fixed positive definite matrix and let $f$ be the function defined by $$f(\Sigma)=\log |\Sigma|+\text{Tr}(\Sigma^{-1}V)$$ over the set $P^+$ of $n\times n$ positive definite ...
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MLE of Geometric variable derived from exponential variable

A call center waiting time is independently distributed $\ \sim \exp( \theta )$, and after some $\ a$ minutes of waiting, the call gets disconnected. After the call gets disconnected, the client ...
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1 vote
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Existence of maximum likelihood estimator in factor analysis

Let $Y_1,\dots,Y_n$ be i.i.d. $N(0,\Sigma$) random variables, where $\Sigma=FF'+ D$ with $F$ $m\times k$ and $D$ is diagonal positive definite. Let $V=\frac{1}{n}\sum_{i=1}^n Y_iY_i^\top$ and define ...
• 3,654
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How do you show the "true parameter" is a critical value of the log likelihood function as n tends to infinity?

These are the first steps in a simple sketch of the proof that, under reasonable conditions, the max likelihood estimate is consistent. I follow the steps all the way down to entering the true ...
1 vote
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(Log) Likelihood as a Loss Function?

I'm trying to understand the relation between the theory of statistical decision problems and the theory of regression of distributions. Recall that a statistical decision problem consists of a ...
1 vote
I am trying to derive the conditional maximum entropy distribution in the discrete case, subject to marginal and conditional empirical moments. We assume that we have access to the empirical moments, $... • 611 1 vote 0 answers 44 views Renewal process with inter-arrival time distributed as gamma: Model estimation Let's start with the Poisson process: If$N_t$is a Poisson process with parameter$\lambda$, then we know that the inter-arrival time distribution is an exponential distribution with parameter$\...
The positive random variables $X_{1}, X_{2},...X_{n}$ are independent and identically distributed as $Ge(\theta)$. The maximum likelihood estimator of $\psi = \frac{(1 - \theta)}{\theta}$ is the ...