# Questions tagged [conditional-variance]

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### GLMs and their conditional expectation and variance

Let the density of the distribution of response $y_i | x_i$ in GLMs denote as: $$f(y; \theta, \phi) = \exp\left(\frac{y\theta - b(\theta)}{\phi} + c(y; \phi)\right)$$ Then conditional expectation and ...
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### Conditional Variance of $Z_i|\sum_i\beta_iZ_i$

Let's assume I have $K$ i.i.d. standard normal random variables $Z_1,...,Z_K$. Hence, I know that $V[Z_i] = 1$ and $E[Z_i] = 0$ for all $i\in K$. I am faced with computing the following conditional ...
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### Regression of squared residuals

I have read in several papers, that one can regress the squared residuals of some conditional mean regression of a variable $X$ on a set of predictor variables and interpret the fitted values as the ...
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1 vote
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### When is it acceptable to compute (conditional) subset-averaged coefficients?

I'm running an ecological study and I have 4 dependent variables (DVs) that I would like to explain (my interest thus lies in inference and not in prediction). For each one of these variables, I built ...
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### Identity of ${{\mathit f}({\mathbf z} {\mid} {\mathbf x)}}$ and ${\mathit f}$($\mathbf {z}$) under normality - a peculiar case

I am a newbie to econometrics, so kindly excuse me if I sound too naive. This is what Fumio Hayashi says on page 34 of "Econometrics": Recall from probability theory that the normal distribution ...
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### Can I predict the variance of a random variable using a machine learning regression model that predicts expected outcomes?

For example, suppose I'm using some machine learning model like gradient boosting that, given some input $x_i$ predicts the expected output $f(x_i) = y_i$. However, I'm also interested in estimating ...
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### The concepts of conditional mean and variance in time series: semantic issues

In time series, the concepts of a "conditional mean" $E_{t}(X_{t+1})$ and "conditional variance" $V_{t}(X_{t+1})$ is semantically unclear to me. Would anyone be able to clearly explain (references ...
1 vote
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### Between-cluster variance in k-means - derivation using total variance

Follow-up to this older post (have to make it a question since I can't post comments yet). Specifically, could anyone kindly show how $$\operatorname{Var}[\operatorname E[X\mid K]]$$ (in total ...
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### Finite second moments inhertitable to conditional variables?

Assume a random vector $\mathbf{x}=(x_1,\ldots,x_n)^\top$ that has finite second moments, i.e., $$\int\mathbf{x}\mathbf{x}^\top\rho(\mathbf{x})\,\text{d}\mathbf{x} < \infty.$$ Does it follow that ...
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### variance of multinomial distribution

Assume $A_{kj} \sim$Multinomial$(1, \;\underbrace{(1/m, 1/m, ..., 1/m)}_{\textrm{m times}})$, where $k=1,2, ... m$ and $j=1,2, ... n$. It is clear to see that $\sum_{k=1}^mA_{kj}=1$. If we impose a ...
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### Is Cov(X,Y|Z).x always positive? (with X,Y,Z, normal random vectors and x>0)

Let x be a vector of positive values, we know that for multivariate normal distributions of X, Y and Z, $Cov(X,Y|Z)x=(\Sigma_{XZ}-\Sigma_{XY}\Sigma_{YY}^{-1}\Sigma_{YZ})x$ does not depend on the given ...
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### Independent variables in the conditional variance GARCH(1,1)

I am using a GARCH(1,1) model, and I would like to add some variables to my conditional variance. I have the data for these variables, but I was wondering if I have to change these variables to ...
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Let $X\in \mathbb{R}$ be a univariate random varible for which it holds that $$X \sim N(\mu,\sigma^2).$$ where $\mu\in \mathbb{R}$ gives the expected value and $\sigma^2>0$ is the variance. If ...