# 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.

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### Likelihood estimation with 2 samples from a geometric distribution

Context Given there are 2 groups that can be modelled as a geometric distribution as follows: \begin{align*} f(x_i;p_1) &= p_1(1-p_1)^{x_i - 1} \; x_i = 1,2,... \; 0<p_1 <1 \\ f(y_i;p_2) &...
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### Marginal distribution of an autoregressive process of order one AR(1)

I'm reading "Econometric Modelling with Time Series" by V. L. Martin, A. S. Hurn and D. Harris ( https://www.researchgate.net/file.PostFileLoader.html?id=56bccdaa6225ff0de28b45a6&...
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### Diagnostic Test needed for ARMAX Model Specification

I'm trying to fit an ARMAX model using forecast::Arima() which is using MLE (https://otexts.com/fpp3/arima-estimation.html). Thus, there is no need for normality test as required by OLS estimator. I ...
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### for linear regression, when is MLE the same as least squares? [duplicate]

Under what conditions is MLE the same as the least squares estimate for ordinary linear regression? I have seen statements saying that these two methods are not entirely the same. But so far, using ...
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### Obtaining MLE of the parameter of exponential distribution

Let say I have a sample of size $n$ as $\{X_1,X_2,...,X_n\}$. The sample points $X_i$ are integers, but each of them are actually integer ceiling of corresponding real number $\{Y_i\}$. For example if ...
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1 vote
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### In MAP, does maximizing the posterior minimize any divergence between distributions?

It's known that maximizing the log-likelihood is equivalent to minimizing the Kullback-Leibler divergence between the model $q(x \mid \theta)$ and the unknown true data generating distribution $p(x)$: ...
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