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Finding the maximum likelihood solution corresponds to finding the root of a regression function. How?

The connection given in Bishop (2006) (p. 96) is that he is implicitly taking: $$z = \frac{\partial}{\partial \theta} \ln p(X|\theta),$$ which then gives: $$\mathbb{E} \bigg[ \frac{\partial}{\partial \...
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Can you have a "PMF-PDF" Together?

This is possible. It is standard measure theory and is done the same way as if all the random variables are continuous or all are discrete: You have a probability space $(\Omega, F, p)$ and your ...
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Is it possible to derive the joint probability distribution of squared OLS residuals under the classical linear regression assumptions?

I've managed to come up with an answer to my question as follows. Bivariate Case Let ${(U_1,V_1),\ldots,(U_k,V_k)}$ be an independent random sample of size $k$ from a bivariate normal distribution ...
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Statistical Models that "Exploit" Distributional Knowledge of the Predictor Variables

In regression models, by definition, we are interested in the conditional distribution of the response variable $Y$ given the observed predictors (covariates) $X$. Namely, if the joint distribution ...
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