Questions tagged [conditional-variance]
26 questions
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How to model conditional variance?
Sorry if this question has been asked before; I'd love to read any discussion around this. There's got to be a better way to summarize this question as well.
I've got covariates $X$ and response $Y$, and suppose I know that when $X$ is high (or…
goopy
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Confusion about parameter covariance using least squares method
I am using the method of least squares to estimate parameter values for a nonlinear model with three parameters: $a$, $b$, and $c$. Call the sum of the squares of the residuals $\chi^2$. I plot $\chi^2$ as a function of $b$ and $c$ at the minimizing…
aFo23
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How to show that an m.d.s is not independent?
I have to prove that this Martingale Difference: $x_t = u_t u_{t-1}$ where $u_t \sim^{iid} (0, \sigma^2)$ is not serially independent, but am failing to do such thing.
I also have to prove that it's conditionally homoscedastic.
What I have tried so…
Caio C.
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Truncated mulitvariate normal: first two moments
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 we are interested in the first two moments of $X$,…
Michael L.
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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 conditional variance of $X$. E.g.:
One can…
shenflow
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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 a set of a priori candidate models based on…
Fanfoué
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Law of Total Variance Issue
The Law of Total Variance says:
if the variance of X is finite then $V(X) = E(V(X|Z)) + V(E(X|Z))$
Suppose $X\sim N(0,1)$, $Y\sim \text{Cauchy}(0,1)$, $X$ and $Y$ are independent.
Define $Z \equiv X + Y$.
In Mathematica & Julia I…
Albert Zevelev
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Conditional distributions of correlated normal random variables
Suppose that $X$ and $Y$ are normally distributed with mean zero and nonzero covariance. I want to know the distributions of $X | X - Y > c$ and $Y | X - Y > c$, which I believe should be jointly distributed as a multivariate normal distribution. I…
quevivasbien
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Modelling the Conditional Variance in a Panel Setting
I am familiar with ARCH-type models to estimate the conditional volatility of some variable of interest in a univariate setting.
I know that there also exists the concept of multivariate ARCH-type models. However, as far as I understand, such models…
shenflow
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Var(e|X), when e=Xu (from Hansen's Econometrics book)
I was working through Bruce Hansen's Econometrics book/notes and got tripped up over something that should be very simple. See the snapshot below, which comes from page 25 of his book Econometrics.
With regards to the variance of e conditional on…
Guinness
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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 has several convenient
features:
• The…
eisendon
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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 the expected variance of each sample input,…
Ben
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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 variance method) is equivalent to $$\sum_k{n_k(\bar x_k…
Tim
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GARCH model with large conditional variance
I have an extremely volatile series (capital flows). Due to heteroskedasticity I tried to estimate GARCH type models.
However, none of the variants (I tried altering process equation, as well as GARCH specification and errors distributions)…
mpmsa2013
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Variance of a normal random variable when conditioning on a correlated normal random variable being above a threshold
Suppose $X$ and $Y$ are correlated with correlation coefficient $\rho$. They are jointly normal with means $\mu_X$ and $\mu_Y$ respectively. Then what is $Var[X | Y \geq T]$? Feel free to add additional assumptions if necessary. $E[X | Y \geq T]$ is…
Johnson
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