Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [maximum-likelihood]

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

In statistics, maximum-likelihood estimation (MLE) is a method of estimating the parameters of a statistical model given data. The method of maximum likelihood corresponds to many well-known estimation methods in statistics. Maximum likelihood, also called the maximum likelihood method, is the procedure of finding the value of one or more parameters for a given statistic which makes the known likelihood distribution a maximum. The maximum likelihood estimate for a parameter $\mu$ is denoted $\widehat{\mu}$.

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Why is $(1/n)\sum_{i=1}^{n}x^T_iMx_i=\operatorname{tr}[1/nx^T_ix_iM]$

I am trying to understand the following identity (context Maximum Likelihood Estiation), where $M$ is the inverse of a symmetric matrix: $$\frac{1}{n}\sum_{i=1}^{n}x^T_iMx_i=\operatorname{tr}\left[\frac{1}{n}x_ix^T_iM\right].$$ I tried this equation…
MrYouMath
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Maximum likelihood estimator of pmf

mle means that maximizer of joint probability mass function. I want to know the mle of theta (4) and Mle of theta (2) I dont know what it means (2) and (4) What i ask you is not same with the question of picture i posted but the data is same. Is…
nien
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Maximum likelihood estmiator of (θ1, θ2)

Given $f(x;θ_{1},θ_{2})=\frac{1}{(θ2-θ1)}$ when $θ_{1}\leq x\leq θ_{2}$ and $0$ otherwise. How would I find the MLE? I know you're supposed to take the $log$ of the likelihood function and then the derivative, but I honestly have no idea where to…
Bbb
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MLE of a parameter $\theta$ which is linear with the observations

Let $Z$ be a single observation having density function $f(z;\theta) = (2\theta z -1 + \theta)$, $0\leq z\leq 1$. Assuming that $\theta$ is a nonrandom parameter and takes values $-1\leq \theta\leq 1$, I try to find MLE of $\theta$ as a function of…
eet
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Find the maximum likelihood estimator (MLE) ψˆ

Let $X =\{X_1,X_2,...,X_n\}^T$ such that $X_i \overset{iid}\sim N\left(\theta,1\right)$. $Y_i=\begin{cases}1,X_i>0\\ 0,\text{otherwise} \end{cases}$ Let $\psi=P(Y_1 = 1)$ Find the maximum likelihood estimator (MLE) $\hat\psi$ of $\psi$. I'm having…
tanvir ahmed
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derive MLE for $\theta$

I want to derive the MLE for theta given this equation $f(x,\theta) = \frac{x}{\theta} \exp \left( - \frac{x^2}{2 \theta} \right)$ do i first take the log and then the derivative of theta?? I think im supposed to get something like…
user14262341
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Likelihood Ratio tests

I am trying to figure out how to calculate an LRT for a question, but my problem seems to start with the fact that I have no idea how this is possible: $$\ln L1 = \ln(100/63) + 63 \ln(1/2) +(100-63)\ln(1-1/2) = -5.92.$$ Regardless of which…
Someone
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