measure_theory
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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:. $$\min_{\beta}\dfrac{1}{... View answer Accepted answer 6 votes If you take the partial derivative of logit(presence) wrt plant you get$$\frac{\partial logit(presence)}{\partial plant} = -32.44 + 15.63*Sobs$$Which means the effect of plant on logit(... View answer Accepted answer 4 votes Not quite. Also note that 9.15537170E+150/1=9.15537170E+150 is far, far greater than one. Probabilities by definition are between zero and one (think percentages). i.e. A goalie can't save 500% of the ... View answer Accepted answer 3 votes It's not true that, with OLS, only the dependent variable, Y, is random. In fact, both can be random variables, however OLS is centered on minimizing the mean squared deviation between Y and X\... View answer 2 votes Like in the other answer, we know that$$f(x\vert a\leq X \leq b) = \frac{f(x)\mathbb{I}_{(a,b)}}{\int_a^b f(x')dx'}$$Where I'm using \mathbb{I}_{(a,b)} as the identity function (i.e. it bounds it ... View answer 2 votes The log-likelihood equation you write is (almost) the log-likelihood equation for a normally distributed distribution with \sigma = 1. The only thing that's throwing me off is the -\log(nRes) ... View answer 2 votes This is a super interesting question/observation.... First thing to note is that$$Var(X_1\mid Z_2) = 1/2$$And the reason that$$Var(X_1\mid X_2) = 3/4 \neq 1/2$$is because it's not possible to ... View answer 1 votes I think you might be referring to the MA(p) terms, which enter the ARMA in an autoregressive way. For example, in an ARMA(1,1) model we have$$Y_t = \alpha + \phi Y_{t-1} + \epsilon_t + \theta\...

I think the most immediate answer is if each function, $g_n$, is continuous. Then, by the continuous mapping theorem, we have that $$X_n\xrightarrow{a.s.}X \Rightarrow g(X_n)\xrightarrow{a.s.}g(X)$$ $$... View answer Accepted answer 1 votes Do you mean two of the independent variables are highly correlated? In that case, the answer is no. Chow's original paper makes no assumption of any independence between the regressors in the model. ... View answer Accepted answer 1 votes Note that$$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)^...

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 ...
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 ...