# Questions tagged [bounds]

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### Bounds on distance between two independently variables drawn from the same distribution

Suppose $X_1$ and $X_2$ are iid from an arbitrary distribution with variance $\sigma^2$. How can we derive an upper bound for: $$P(|X_1-X_2|\ge\delta)$$ One simple idea is Chebyshev's Inequality, ...
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### Are there supposed to be bounds on parameters in 2PL Item Response Theory models?

Recently I've been studying Item Response Theory (IRT) and have come across some issues with the application side of it. I currently have a dataset of ~200 respondents x 7405 questions (quite ...
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### What is a common-sensical approach to setting the boundaries of an interval?

As I am trying to present my results to a non-expert audience, I am wondering about what the most commonly used boundaries are for intervals. I mean specifically, which of the four versions explained ...
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### How to bound a regressor function?

I've seen similar questions on here, but none seem to quite apply to my use case. I want to predict Metacritic scores bases on a number of features. Metacritic scores are bounded to a 0-100 scale, ...
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### Use Chebyshev's inequality to ﬁnd a lower bound of a Chi-Square Distribution

I'm trying to solve the following exercise but I'm not sure if what I'm doing is right. "Let $X$ be an r.v. distributed as $\chi_{40}^{2}$. Use Tchebichev’s inequality in order to ﬁnd a lower ...
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### the approximation of the variance of MLE (Cramer-Rai Lower Bound)

This is in In Casella's Statistical Inference，page 473, the approximation of the variance of MLE (Cramer-Rao Lower Bound). I really confused with the conclusion: $Var_{\hat{\theta}}h(\hat{\theta})$ ...
I have a dataset $\mathbf{X} = \{ \mathbf{x_1},\mathbf{x_2},...,\mathbf{x_n} \}, x\in\mathcal{R}$ with length $n$ and dimension $d$ along with corresponding labels $\mathbf{y}, y \in \mathcal{R}^+$. ...