measure_theory
  • Member for 5 years, 3 months
  • Last seen this week
  • New York, NY, United States
Why do we care about Quasi-norm in Statistics and Machine Learning?
Accepted answer
6 votes

One common area where quasinorms are used involves dimension reduction and sparsity. Consider Lasso, where the standard OLS problem is augmented by a penalty, or cost term:. $$\min_{\beta}\dfrac{1}{...

View answer
Why does sign of a main effect change in logistic regression when adding an interaction?
Accepted answer
6 votes

If you take the partial derivative of $logit(presence)$ wrt $plant$ you get $$\frac{\partial logit(presence)}{\partial plant} = -32.44 + 15.63*Sobs$$ Which means the effect of $plant$ on $logit(...

View answer
the very basic probability on not being born in May
Accepted answer
4 votes

Not quite. Also note that 9.15537170E+150/1=9.15537170E+150 is far, far greater than one. Probabilities by definition are between zero and one (think percentages). i.e. A goalie can't save 500% of the ...

View answer
Linear regression and interpretation of random variables
Accepted answer
3 votes

It's not true that, with OLS, only the dependent variable, $Y$, is random. In fact, both can be random variables, however OLS is centered on minimizing the mean squared deviation between $Y$ and $X\...

View answer
Expected value of $X$ which follows a normal distribution, between a certain interval
2 votes

Like in the other answer, we know that $$f(x\vert a\leq X \leq b) = \frac{f(x)\mathbb{I}_{(a,b)}}{\int_a^b f(x')dx'}$$ Where I'm using $\mathbb{I}_{(a,b)}$ as the identity function (i.e. it bounds it ...

View answer
Determination of maximum log-likelihood of nonlinear model for calculation of Aikaike IC
2 votes

The log-likelihood equation you write is (almost) the log-likelihood equation for a normally distributed distribution with $\sigma = 1$. The only thing that's throwing me off is the $-\log(nRes)$ ...

View answer
Peculiar Behaviour of Conditional Variance for Multivariate Normal Distributions
2 votes

This is a super interesting question/observation.... First thing to note is that $$Var(X_1\mid Z_2) = 1/2$$ And the reason that $$Var(X_1\mid X_2) = 3/4 \neq 1/2$$ is because it's not possible to ...

View answer
ARMA models and residual series
1 votes

I think you might be referring to the MA(p) terms, which enter the ARMA in an autoregressive way. For example, in an ARMA(1,1) model we have $$Y_t = \alpha + \phi Y_{t-1} + \epsilon_t + \theta\...

View answer
Conditions for convergence of transformed random variables?
1 votes

I think the most immediate answer is if each function, $g_n$, is continuous. Then, by the continuous mapping theorem, we have that $$X_n\xrightarrow{a.s.}X \Rightarrow g(X_n)\xrightarrow{a.s.}g(X)$$ $$...

View answer
Does the Chow test require the independent variables to be uncorrelated?
Accepted answer
1 votes

Do you mean two of the independent variables are highly correlated? In that case, the answer is no. Chow's original paper makes no assumption of any independence between the regressors in the model. ...

View answer
Taking out matrix from variance operator
Accepted answer
1 votes

Note that $$Var(A^Te\vert X) = \mathbb{E}[(A^Te)(A^Te)^T\vert X]$$ Assuming $\mathbb{E}(e)$ is a vector of zeros. So by expanding the above we see that: $$Var(A^Te\vert X) = \mathbb{E}[(A^Te)(A^Te)^...

View answer
What is the proper interpretation of the slope of the regression equation?
0 votes

When central pressure increases by one unit, measured win speed decreases $0.897$ units. When central pressure decreases by one unit, measured wind speed increases by $0.897$ units. Also notice ...

View answer
Predicting using GLS
0 votes

There are a few ways to judge how well your model for Island $i$ performs on Island $j$, but the simplest might be to calculate and compare the $R^2$, which tells you the ratio of the variance ...

View answer