# Questions tagged [bounds]

The tag has no usage guidance.

238 questions
Filter by
Sorted by
Tagged with
6 views

### Unbounded function with finite integral [migrated]

I am facing the following condition in order to apply a theorem in a paper: $$\int_{\mathbb{R}}\left[\phi^{\prime}\left(|x|^2 / 2\right)\right]^4(1+|x|)^{-\nu_2} d x<\infty.$$ It is stated the if ...
• 73
117 views

### Upper bound for m.g.f

$X$ is a discrete random variable from power series family (e.g., binomial, poisson etc.). is it possible to find an upper bound for the m.g.f of $X$? N.B: from stack exchange I obtained the following ...
• 75
19 views

### Relationship between P-value (ANOVA) of subsets of dataset

I'd like to ask this as a general question, but it originated from a specific situation I came across. Let $\mathcal{D}$ be a dataset. Each point has two attributes, $X$ and $Y$, and a corresponding ...
• 125
46 views

### Relation between generalization bounds of Kernel Ridge Regression and largest eigenvalue of the kernel Gram matrix

Consider a positive-definite, symmetric function $k(x_1, x_2)$ which is used, given the dataset $\{(x_i, y_i)\}_{i=1}^m$, to construct the Gram matrix $K = [k(x_i, x_j)]_{i,j \in 1, ..., m}$. What is ...
• 31
1 vote
26 views

36 views

### Fixed-leg Kalman filter smoother (Rauch–Tung–Striebel) error bounds

Although very intuitive and with plenty of results that talk about the asymptotic convergence of the estimate I wasn't able to track down any paper stating explicitly convergence bounds based on the ...
• 1
21 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 ...
37 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 $y_A$ ...
• 1,621
169 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'...
16 views

### Bounds on Ratio of Likelihood to Marginal?

Bayesian inference tells us that the posterior over parameters $\theta$ given data $X$ is given by: $$p(\theta|X) = \frac{p(X|\theta)}{p(X)} p(\theta)$$ Are there any known bounds on the ratio of the ...
1 vote
40 views

• 179
64 views

### 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 ...
• 21
1 vote
19 views

### 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....
• 1,072
1 vote
129 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 ...
• 23
48 views

### 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 ...
• 31
153 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:...
• 27.8k
311 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 ...
• 89
174 views

### Interpretation of upper bound on the Wasserstein Distance

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 ...
• 175
80 views

1 vote