All Questions
Tagged with upper-lower-bounds statistics
56
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Hoeffding's Inequality Assumptions
I'm looking for the assumptions of the Hoeffding's inequality to check it is applicable to my problem. So far the only assumptions I can find are the variables $Z_i$ are IID and bounded. However, Im ...
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On the difference between the main effect in a one-factor and a two-factor regression
This question was asked on Cross Validated where it received little attention and no comments or answers, but as it is purely mathematically oriented it may well be more suitable here.
Consider a ...
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Markov Inequality question confusion bound problem
"If a fair die is rolled 200 times, count the number of 1’s. Give an upper bound for the probability that the count of 1’s stays below 8. "
So here for Markov inequality,
P(X>=8)<=E[X]/8.
So here,...
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How to find upper bound of a probability?
We roll a fair die 50 times and count the number of 2’s. Give an upper bound for the probability that the count of 2’s stays below 7.
How can I approach this problem?
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High probability upper bound for linear combination of Gaussian random variables
Suppose that $x_1, \dots, x_n$ are i.i.d. with $x_i \sim N(0,I_k)$. Let $A_1, \dots, A_n$ be matrices with dimension $k \times k$ and $\|A_i\|_2 \leq 1$. Consider the following random vector
$$y = \...
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Nice bounds for 3rd folded central moment in terms of variance?
Say we have some real numbers $x_1, \ldots, x_n$, and let $\mu$ be their mean and $\sigma^2$ be the variance. Are there some nice bounds for $\frac 1n \sum_{i=1}^n |x_i - \mu|^3$ based on $\sigma^2$? ...
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Show that $\operatorname{Pr}(Z-X \geq 0)$ converges to one
Suppose that $V_i$, for $i \in \mathbb{N}$, are i.i.d. standard normal random variables and $Y_i = \sum_{k=1}^i V_k$ for $i \in \mathbb{N}$ with $Y_0 = 0$. Let $X_n = (\sum_{i=1}^n V_i Y_{i-1})^2 Y_n^...
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Showing that the following ratio expectation is bounded by $O(1/n)$
Suppose that $V_i$, $i \in \mathbb{N}$ are i.i.d. standard normal random variables and let $Y_i = \sum_{k=1}^i V_i$ for $i\geq 1$ and $Y_0 = 0$. Consider the following ratio random variable
$$R = \...
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662
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VC dimension of a circle
I have a circle where all the points inside a circle are labelled positively and all the points outside the circle are labelled negatively. The center of the circle is h and radius is r. Let H+ be ...
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Upper bound for variance of kernel averages
I'm reading Hansen's (2008, p. 729) Theorem 1 where he bounds the variance of averages of the form
$$\hat\Psi(x)=\frac1{Th}\sum\limits_{t=1}^T Y_t K\bigg(\frac{x-X_t}h\bigg)$$
given that $\{(Y_t,X_t)\...
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How concentrated is the $t^{th}$ smallest discrete uniform order statistic?
Let $n,z,t$ be positive integers and let $X_1,\ldots,X_{z\cdot t}$ be i.i.d. random variables that are uniformly distributed over $\{0,\ldots,n\}$.
Let $X_{(t)}$ denote the $t^{th}$ smallest ...
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Probability. Define Upper bound and Lower bound for double integral. [closed]
I am finding trouble of finding bounds for double integral for statistic.
Here the question looks like:
given joint pdf = $\frac{3x}4$, $0<x<1,\;0<y<4x$.
I have to find pdf of $R=XY$.
...
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Upper bound for Variance of linear combination of random variables: $\operatorname{Var}\left(x^Ta\right) \leq \frac{\|a\|^2}{4}. $
I found this while reading a paper where they used it as a casual fact.
Say, you have a vector $x = (x_1, x_2, \dots, x_n)$ where $x_i \in [0,1]$ are independent random variables. Consider linear ...
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Is there a way to bound expected value with limited information of the CDF?
Suppose I want to evaluate $E[X]$, where $X$ is a univariate random variable and takes values in $\mathcal{X}$, where the smallest element of $\mathcal{X}$ is 0 and the largest element of $\mathcal{X}$...
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upper bound on cross entropy or relative entropy
Am looking for upper bounds for relative-entropy or cross-entropy for non-gaussian case . All I am aware of is bounds for entropy based on determinant of covariance matrix.
What about for relative ...
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