# Questions tagged [bounds]

Bounds represent the points with which data cannot exceed, such as minima or maxima.

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### Calculating variance between paired samples, where one sample is constrained to always be the lower bound?

I'm sure this is a solved question, but I haven't been able to hit on the right search terms. Suppose I have paired samples A and B. A represents a derived variable (say distance "as-the-crow-...
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### Bound Product of Independent Gaussians

I'm interested in obtaining upper bounds on $$\Pr[\prod_{i\in[n]}|G_i| > x]$$ where $G_i\sim\mathcal{N}(0,1)$ i.i.d, and $[n] := \{0,1,\dots,n-1\}$. The most naive bound is to note that each $G_i$...
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### Bound on Rademacher complexity using polynomial discrimination

This is lemma 4.14 in Wainwright's textbook on High-Dimensional Statistics, it states that given a class of function $\mathcal{F}$ has polynomial discrimination of order $v$, then for all integer $n$ ...
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### likelihood ratio tests on bounded parameters

I am confused by the likelihood ratio test's boundary condition limitation. A commonly stated is that it causes problem for variance parameter because it is bounded below by 0. Can these models ...
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### Validity of Bootstrap Inference for Bounds

I am facing the following problem: I have access to iid $X_1,\dots ,X_{N_X}$ and $Y_1, \dots, Y_{N_Y}$ from $F_X$ and $F_Y$, respectively, where $X$ stochastically dominates $Y$. My goal is to conduct ...
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### How to bound neural network output?

I have a NN with a single output scalar. I want this scalar to tend towards positive infinity if some of the inputs take on certain values. How can I guarantee this without adding training data?
1 vote
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### Number of samples for Hoeffding's Bound with Gaussian R.V

I am trying to obtain the required number of sample $n$ for a given confidence interval $\alpha$ and $X_1 ... X_n$ which are Gaussian rv with $\mu$ mean and $\sigma^2$ variance. I know that \begin{...
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### What can be concluded when standard deviation plus mean exceeds largest value?

The sum of the mean and standard deviation of a non-normal distribution can exceed the value of the largest sample. For a good explanation of why, see Can mean plus one standard deviation exceed ...
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### Why is the lower bound of the confidence interval of a model's error relatively constant compared to the upper bound? [closed]

I am interested in studying the effect of increasing data samples for a regression model on train error and test error. For this I have used 95% confidence intervals for different values of a sample ...
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### What is the definition and upper bound on the variable "m" in the definition of the multivariate normal Fisher Information?

Multivariate normal distribution  The FIM for a $N$-variate multivariate normal distribution, $X \sim N(\mu(\theta), \Sigma(\theta))$ has a special form. Let the $K$-dimensional vector of ...
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### How to compute a non-trivial lower bound on $P \left[|X| > \frac{|\alpha|}{2} \right]$?

Let $X$ be a random variable such that $E[X] = \alpha$, $\alpha \in \mathbb{R}$ and $E[X^2] = \beta$. The problem is to find a lower bound on the following probability  P \left[|X| > \frac{|\...
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### What is the probability that every variable of combination of random variables is greater than a specific value?

Suppose there are $N$ positive random variables. Each variable follows an exponential distribution with parameter $\lambda_i$. Now, we choose $n$ variables among the $N$ variables. What is the ...
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Suppose we have the sum $$\sum_{t=2}^{n}\epsilon_{t-1}u_t$$ where $\epsilon_t$ and $u_t$ are both sub-Gaussian variables. Further suppose that while $u_2,\cdots,u_n$ are i....