# Questions tagged [bounds]

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

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### Bound on the expectation of a function of random variable having a strictly log-concave probability density

let $\theta \in \mathbb{R}^d$ be a random variable having a strictly log-concave probability density function, i.e \begin{equation} p(\theta) = e^{-\phi(\theta)} \end{equation} where $\phi(\theta)$ is ...
36 views

### Bound over sample probability

I have a discrete random variable $x \sim \text{Cat}(\textbf{p})$. What I'm trying to compute is the probability that any sample $x$ has an associated probability of at least $\alpha$. I would compute ...
61 views

### Is this derivation in Manski (1990) correct?

Consider the following setting. There are two treatments, $A,B$. Individuals in the population are described by a tuple $(y_A,y_B,z)$ where $z \in \{A,B\}$ denotes the treatment received. Only $y_A$ ...
503 views

### Given a correlation between A and B, what are the best bounds on the product of the AC and BC correlations?

Let's say I have three vectors (or random variables) $A, B,$ and $C.$ I can of course calculate the correlation between any of them (and have these numbers). However what I'm interested in is if there'...
1 vote
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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 ...
1 vote
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### Lower bounding the sum of product of two sub-Gaussian variables where one follows an AR(1) process

Suppose we have the sum \begin{equation} \sum_{t=2}^{n}\epsilon_{t-1}u_t \end{equation} where $\epsilon_t$ and $u_t$ are both sub-Gaussian variables. Further suppose that while $u_2,\cdots,u_n$ are i....
1 vote
287 views

### Predicting limits of bounded dependent variable in Random Forest

I am new to machine learning and trying to use Random Forest to predict a bounded dependent variables (percentage from 0 - 100). The majority of the training data points (~80%) are at the limits of ...
1 vote
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### How to find the bound of a time dependent variable?

I am working on modeling my problem statistically and I need to Know the bound or range of my variable. It is a time series variable position(t) where position(t+1) = position(t) + a.X - (1-a).Y a is ...
166 views

### Bounding sum of quartic deviations from sample mean

[Cross-posted here with no answers for a few days] I came - to the very best of my knowledge from reading the source - across the following statement in The Jackknife and Bootstrap, Shao and Tu, p. 87:...
642 views

### Can we find upper bound for loss functions?

Is it easy to find upper bound for loss functions like 0-1 loss and hinge loss ?!. I always find this sentence, which is "hinge loss is an upper bound of 0-1 loss", Can we compute the upper ...
I am trying to interpret the 2-Wasserstein distance and the upper bound on it. Let's say I have 2-Wasserstein distance between two distributions to be $x$, and I have an upper bound on it which gives ...