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1

Something strikes me as particularly odd when comparing different likelihoods via AIC. Suppose I observed $x=2$. The log likelihood for a gaussian, gamma, and poisson each with mean and variance 1 is -0.91, -1, and -1. Should I assume this observation came from a gaussian simply because of the likelihood, ignoring details about the data generating ...

2

Pearson Residuals As tosonb1 points out, "The Pearson residual is the difference between the observed and estimated probabilities divided by the binomial standard deviation of the estimated probability". I just wanted to mention that Pearson residual is mostly useful with grouped data i.e, say, there are $n_i$ trials at setting i of the explanatory ...

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You are comparing LASSO and subset selection. It is not quite clear how you tune the penalty intensity of LASSO$\color{red}{^*}$, while for subset selection you use AICc as the criterion. It seems you are only considering nested models in subset selection. E.g. you select between models with lags $\{1\}$, $\{1, 2\}$ or $\{1, 2, 3\}$ but not $\{2\}$ $\{3\}$, ...

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Answers here advises against variable selection, but the problem is real ... and still done. One idea that should be tried out more in practice is blind analyses, as discussed in this nature paper Blind analysis: Hide results to seek the truth. This idea has been mentioned in another post at this site, Multiple comparison and secondary research. The idea ...

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I've thought about this a lot (I am OP), and I've come up with the following conclusion through my readings: Consider RV $X$ distributed wrt a density $f(x\mid\theta_0)$ (some observed) Here we assume the data can be generated through a parameterization (justify the presence of conditioning), and that in particular samples wrt $X$ are generated wrt a true ...

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I think you are correct: strictly speaking there should be no $\mathbb{E}$ before the integral term (which, by the way, also appears in equation 1.2, but not in equation 2.1). There is one way to see it: the best estimate $\hat{\theta}$ of the ground truth value $\theta$ will be the one that will minimize the Kullback-Leibler divergence between the estimated ...

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I imagine they made an approximation. $\sigma^2_\epsilon$ is the residual variance of the outcome conditioned on the variables $x_i$. When the outcome is binary, as in logistic regression, $\sigma^2<1$. When we compare models with AIC, only the absolute differences between models matter, so using the approximation $\sigma^2=1$ for all models isn't so ...

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