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.
3,489 questions
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Model comparison with different fixed effects - LMM
I tried to find answers to this, but couldn't manage to do so. So in my research, one of the main questions that I have is to assess the effects of these three food groups (milk, grain, and vegetables)...
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Estimation of many Gaussian process hyper-parameters
I am working with a Gaussian process $(X_t(x))_{x \in [0,1], t \geq 0}$ which evolves jointly in space and time. I know the statistics of this process: $\mathbf{E} X_t(x) = X_0(x) e^{-\mu r t} + (1-e^{...
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Maximum likelihood estimation for linear regression [duplicate]
When conducting maximum likelihood estimation for simple linear regression whilst considering the regressors as random, the joint distribution of $f_{X,Y}(x,y;\theta) = f_{Y|X}(y|x;\theta) * f_{X}(x;\...
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Maximum Likelihood estimation for heavy tailed and binned data
I have binned loss data where each bin is defined by:
A minimum loss and maximum loss (the bin boundaries)
A probability of occurrence for that bin
The probabilities across all bins sum to 1. ...
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In a heteroskedastic model, can I treat the first term $ (y_{1}-\mu)^2 $ as a weighted term with weight 1?
I’m working on an MLE exercise for the following model:
$$
Y_{1} \sim \mathcal N(\mu,\sigma^2), \qquad
Y_{i} \mid Y_{i-1}=y_{i-1} \sim \mathcal N\!\big(\mu,\ \sigma^2(1+y_{i-1}^{2})\big),
\quad i\ge 2 ...
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1
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Maximum likelihood estimation with the likelihood function as a function of random variables
I have seen many texts use this notation where they define the likelihood function as a function of random variables and the unknown parameter, rather than a function of the data and the unknown ...
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Asymptotics in case of non-identifiability
I am dealing with a situation, where my distribution, becomes non-identifiable with respect to the parameters. Can anyone suggest some reliable sources or references wherein I can find the asymptotic ...
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Are lag vectors in time series MLE just measurable functions in Newey & McFadden’s ergodic ULLN?
In Newey & McFadden (1994), Large Sample Estimation and Hypothesis Testing (Handbook of Econometrics, Ch. 36), they extend ULLN results from i.i.d. data to stationary ergodic sequences, e.g.:
“...
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How to perform a sensitivity analysis in statistics?
I am trying to understand how to study/diagnose the identifiability of statistical models (i.e. how well can parameters be uniquely estimated). So far my findings include:
Examine the identifiability ...
user491065
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Writing the profile likelihood in R
Here is the log-likelihood of a two component normal mixture model:
$$\ell(\theta | x_1, ..., x_n) = \sum_{i=1}^{n} \log\left[ \pi \frac{1}{\sqrt{2\pi\sigma_1^2}} \exp\left(-\frac{(x_i-\mu_1)^2}{2\...
user491065
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Maximum Likelihood Estimation - How Reasonable is the Assumption of Independence?
In the context of multiclass supervised classification, given $N$ samples which are feature-label pairs $\{(X_1, y_1), \ldots, (X_N, y_N) \}$, maximum likelihood estimation (MLE) seeks to maximize the ...
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How to use profile likelihood to determine identifiability?
This is a follow up from my previous question Why is the profile likelihood used to determine if a model has a unique solution? . I am interested in knowing how Profile Likelihood can be used to ...
user491065
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Why is the profile likelihood used to determine if a model has a unique solution?
I have seen different materials online (e.g. https://www.youtube.com/watch?v=wi6narLrvP4, https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011515) which show that the profile ...
user491065
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How to estimate probability of an element being erased from observatios
I have a set of observations with different number of elements, let's say $\textbf{o}_1=\{a,b\}$ ($2$ times), $\textbf{o}_2=\{b, c\}$ ($1$ time), $\textbf{o}_3=\{d\}$ ($4$ times). The original set ...
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Loglikelihood of fit over power-transformed data (power $p$) constant accross $p$?
Just consider data x and its powers x^p. I wanted to check the impact of p on the goodness ...
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