# Questions tagged [maximum-likelihood]

a method of estimating parameters of a statistical model by choosing the parameter value that optimizes the probability of observing the given sample.

2,291 questions
Filter by
Sorted by
Tagged with
7 views

### Fitting mixture model on data with duplicate values

What is the correct procedure to fit finite mixture models on data with many duplicate values using EM? Let's say I have N(0,1) distributed data and try to fit a 2 component mixture using EM. There ...
57 views

### Why can't regression via Maximum Likelihood shrink coefficients to zero?

Why can't regression via Maximum Likelihood shrink regression coefficients to zero as in LASSO? Does shrinking coefficients to zero not give higher L-likelihood? Does the answer to my question have to ...
17 views

### Does the newton-raphson either find the maximum of the loglikelihood function or estimate the MLE and likelihood function? [closed]

Does using newton-raphson method or some other optimization method used in nlme package or mixed effects models actually find the maximum of the log-likelihood function's height or does it simply find ...
5 views

### Indefinite Hessian in Negative Binomial log-likelihood estimation

I have the following problem: I am estimating a Negative Binomial regression. In order to estimate the model, I implemented the Newton method from the scratch. I am optimizing the dual of the log-...
18 views

### Maximum likelihood and Minimizing Kullback–Leibler divergence to the ecdf?! (i.e.: finite sample statement?)

There is a known relationship stating that finding MLE is asymptotically the same is minimizing Kullback–Leibler divergence (see wiki here), or just the cross entropy. I'm wondering if there is a ...
32 views

### Difference Between $L(θ | X=x)$ and $P(θ | X=x)$? [closed]

Although statistically different, I feel like they both say the same thing? $L(θ | X=x)$ = the probability that a sample provides support for particular values of a parameter in a parametric model. ...
16 views

18 views

### why the sigma(volatility) is so small when useing the maximum likelihood estimation for vasicek model

This is my monthly data(in percentile)-2year japan government bond's yield to marturity from year 2001 to year 2019.And my LL function comes from "Maximum likelihood estimation using price data of the ...
37 views

### Assumption of error of logistic regression [duplicate]

I know there are debates about whether the error exists and its distribution in the case of logistic regression. Suppose we assume that the error term follows the logistic distribution. Are we ...
9 views

### Manual calculation of logit regression [duplicate]

I have been working on Logit regression and I don't understand how to find coefficients by hand. I have seen that its possible to do it using maximum likelihood but I don't have much background in ...
21 views

### Fisher matrix with penalty function

I am fitting a parametric model to human tracking data. Because my data is in part corrupted (see below why), as such I had to introduce a penalty function to my optimization algorithm. The Fisher ...
51 views

### how to set the parameter constraints in maxLik() in R [closed]

question: how to use maxLik() to set the constraints? For example,the beta and alphh should >0, and sigma should >=0.0001 .The following is my code, and it doesn't work in mle<-maxLik(...),because ...
37 views

### Constrained MLE

How to write R-code for obtaining MLEs of a ,b and $\theta$ for the density function \begin{equation} f(x)=\theta(a+bx)e^{-(ax+\frac{1}{2} b x^2)}\left(1-e^{-(ax+\frac{1}{2} b x^2)}\right)^{\theta-1} \...
24 views

### Re-writing the Score Test Statistic [closed]

We all know that the formula of the score test is: $$S = \frac{\{l'(\theta_0)\}^2}{E\{-l''(\theta)\}\bigg|_{\theta_0}}$$ where $l'$ and $l''$ are $log$ $likelihoods$ What I need to do is represent ...
54 views

29 views

### Extend likelihood equation to P(Y>=y) in R

This question involves both math and coding in R. Apologies if this should be on Stack Overflow, but I decided statisticians would ultimately provide better support....
42 views

### Bayesian random variables VS. MLE fixed variables

"Bayesian inference treats model parameters as random variables whereas frequentist inference considers them to be estimates of fixed, ‘true’ quantities." (Ellison 2004) What does it mean in the ...
35 views

### “Explanation power” of a parameter [closed]

Suppose there are two practically similar statistical models with similar "breath": $L(\theta)$ and $M(a,b)$, where $\theta, a, b$ are parameters. When fitting with data, if we assume that $b$ is ...
31 views

### MLE $\hat{h(\mu)} = h(\hat{\mu})$ of $h(\mu) = var(Y_1) = \mu^2$

Question: Suppose Y1, · · · , Yn follows an Exponential distribution with $\lambda = \frac{1}{\mu}$. Derive the MLE $\hat{h(\mu)} = h(\hat{µ})$ of $h(µ) = var(Y_1) = µ^2$, and show that $h(\mu)$ is ...
Each book I read propose a different fitting method for Logistic Regression. The general idea is to maximize this expression. $$Pr\left(\beta|y,X,M\right) = \frac{Pr\left(y|\beta,X,M\right) Pr(\... 0answers 77 views ### Parameter estimation when the likelihood function does not exist The observations Z_1,Z_2\cdots are i.i.d. We have$$Z_k = \sum_{i=1}^\infty \frac{X_{ki}}{2^k}.$$where the X_{ki}'s are i.i.d. with a Bernouilli(p) distribution. If p=\frac{1}{2} then Z_k ... 0answers 21 views ### MLE vs MAP hypothesis, performance I have a question regarding the performance of Maximum a posteriori vs Maximum Likelihood Estimation hypothesis. If you only consider the training data. Can you then state that the MAP hypothesis ... 2answers 83 views ### Can an improper prior distribution be informative? I have just worked through an example where, with an improper prior, the bayesian estimator equals the maximum likelihood estimator, leading me to believe that improper priors are uninformative. But ... 1answer 46 views ### Invariance of maximum likelihood estimates to rearrangements of parameters/constants in the model? I know that maximum likelihood estimates are invariant to re-parametrization (https://stats.stackexchange.com/a/335368/267430). Is the MLE also invariant to rearrangements of the constants and ... 1answer 46 views ### Question about Casella and Berger's proof of MLE invariance In Casella and Berger, p. 320, they have a proof of the invariance of the MLE. Let g: \theta \mapsto \eta be a function. They define the induced likelihood as$$ L^*(\eta \mid X) = \sup_{\{\theta: ...
Consider a single-parameter distribution and a two-sided test for hypothesis $\theta_0$. Does the likelihood ratio test just reduce to:  \frac{\max_{\theta \in \Theta_0} \mathcal{L}(\theta)}{\max_{\...