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2

Rather than a problem with multicollinearity, I suspect that in your cross-validation (CV) you end up with some data folds that lack events for at least one level of one or more categorical predictors in the fold's training set. In that case the Cox model will not converge for that fold. One way to proceed in general would be to build a try/catch step into ...


0

And could one also write that $(\hat{X}_n - \bar{x}) = o_p(1)$ is equivalent to $\hat{X}_n = \bar{x} + o_p(1)$? I do not know whether this is conventional, but you can do it. Interpretation in terms of quantile functions We can argue about these notations with $o_p$ and $O_p$ in the same way as for $o$ and $O$ when we make an interpretation that connects ...


5

Yes, $X_n-\bar x=o_p(1)$ is just notation for saying "For every $\epsilon>0$, $$\lim_{N\to\infty}P\left(|X_n-\bar x|>\epsilon \right)=0"$$ More generally, $X_n-Z_n=o_p(Y_n)$ is notation for saying "For every $\epsilon>0$, $$\lim_{N\to\infty}P\left(|X_n-Z_n|>\epsilon |Y_n| \right)=0"$$


0

Let $Y_n = \frac{|X_n|}{1+|X_n|}$. Then $Y_n$ is bounded above by 1. For $\epsilon\gt0$, $$ \begin{align}\mathbb{E}(Y_n)&\leq \left(\mathbb{P}(|X_n|\lt\epsilon)\sup_{|X_n|\lt\epsilon}Y_n\right) + \left(\mathbb{P}(|X_n|\ge\epsilon)\sup_{|X_n|\ge\epsilon}Y_n\right)\\& \leq\left(\sup_{|X_n|\lt\epsilon}Y_n\right)+\mathbb{P}(|X_n|\geq\epsilon)\\ &= \...


1

This answer is part of a previous answer with a link here. That portion of the previous answer is copied over here so that one can see that the question above has been answered, however, as the answer here formed only part of an answer to a different question, it might not have been noticed in the different context of the question above. Text as follows: A ...


3

Z-transform exists because for $n<0$, $|n|=-n$, the mistake is in in your second line (in the eq): $$\begin{align}X(z) &= \sum_{n=-\infty}^{0}2^{n} z^{-n} + \sum_{n=1}^{\infty}2^{-n} z^{-n}\\&=\sum_{n=0}^\infty (z/2)^n + \sum_{n=0}^\infty (1/2z)^n-1\\&=\frac{1}{1-z/2}+\frac{1}{1-1/2z}-1\end{align}$$ And the ROC is $|z/2|<1 \cap |1/2z|<1\...


0

In short You can express a lower limit for the probability that $Y_n X_n$ is within some boundary $\epsilon = \epsilon_y \cdot \epsilon_x$ by the product of the probability that $Y_n$ is within some boundary boundary $\epsilon_y$ (which can be made as close to 1 as you like by increasing $n$ and $\epsilon_y$) and the probability that $X_n$ is within some ...


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