All Questions
3
questions
1
vote
0
answers
48
views
Upper Bound for Moments for Product of Sample Means
I have a question about the upper bound of the following moment.
Suppose that $(A_1, e_1),\ldots, (A_n, e_n)$ are i.i.d. with $E(e_i)=0$. I am wondering if we have the bound
$$E\bigg(\bigg\|\frac{\...
- 53
1
vote
1
answer
47
views
Variance of sum of deviations
Suppose I have an i.i.d. sample $\{X_i\}_{i=1}^M$ for some positive integer $M$, and suppose that $X_i \sim X$ for some random variable $X$ with finite variance. Then, denote by
$$
E_M = \frac1M\sum_{...
- 1,450
0
votes
1
answer
49
views
$\max_{\{X_N\}}{\frac{\mu^2(X_N)}{\mu^2(X_N)+\sigma^2(X_N)}}$ for $X_N=\{x_1,...,x_n\},x_i\in \mathbb{N}^+,\exists(i,j):x_i\neq x_j$
Short version of the question
Consider
\begin{equation}
g(X_n)=\frac{\mu^2(X_N)}{\mu^2(X_N)+\sigma^2(X_N)}\\
X_N=\{x_1,x_2,...,x_n\},n>1,\forall i:x_i\in \mathbb{N}^+,\exists(i,j):x_i\neq x_j
\end{...
- 401