Tagged Questions
0
votes
0answers
17 views
Help with an asymptotic proof? [duplicate]
I am having difficulty with a proof of an asymptotic result in maximum likelihood estimation theory. I don't believe any statistical theory however is needed to solve this problem, rather I think ...
2
votes
1answer
40 views
Question on Convergence in Probability
I appreciate if you could guide me on this question:
Assumptions:
$X_n \rightarrow^p c$: $X_n$ convrges in probability to a constant c.
g(.) is any function that satisfies:
$$\text{if } a_n - c = ...
10
votes
2answers
198 views
Asymptotics of the sum of squares of binomial coefficients
We are trying to estimate the cardinality $K(n,p)$ of so-called Kuratowski monoid with $p$ positive and $n$ negative linearly ordered idempotent generators. In particular, we are interesting in the ...
1
vote
0answers
68 views
Large Deviations Problem
Let $\left(X_n\right)_{n\geq 1}$ be i.i.d random variables on $\left(\Omega,\mathcal A, \mathbb P\right)$, $X_1$ with mean $\mu$, and
$$
L(\lambda) =
\begin{cases}
\log\mathbb E\left(e^{\lambda ...
10
votes
1answer
141 views
Calculate Asymptotics of Integral?
Let $f$ be a continuous function on $[0,1]$. How do I calculate the asymptotics, as $n\rightarrow\infty$, of
$\displaystyle \int_{[0,1]^n}f\left(\frac{x_1+...+x_n}{n}\right)\text d x_1...\text d ...
0
votes
0answers
22 views
Gärtner-Ellis for Matrices?
Is there a version of the Gärtner-Ellis Theorem that can deal with matrices? And if there is, do you know where I can find it? Thank you for your help!
My problem is that I have a sequence of ...
0
votes
1answer
49 views
Asymptotic Notation more specifically, Big-O notation
How the functions in the class $O(d)^d$ and $\epsilon^{1/O(d.4^d)}$ looks like..?
where $\epsilon$<1.
I am really confused with this complicated Big-O notations
Can you please help me out.
2
votes
2answers
141 views
Help with the integral for the variance of the sample median of Laplace r.v.
When we draw $n$ samples of Laplace-distributed random variable such that $n=2k+1$ and the location parameter is zero, the median $x$ (or the $k$-th order statistic) has the following p.d.f.:
...
0
votes
0answers
40 views
understanding of 1-unconditionality
Let $X=(X, \|\cdot\|_X)$ be normed space with $x_1, \ldots, x_m\in X$.
Assume, $\int_{[-1,1]^m}\|\sum_{i=1}^ma_ix_i\|_Xd\mu(a)=1$, where $\mu$ is the Lebesgue measure on $[-1,1]^m$, $a \in [-1,1]^m$.
...
2
votes
0answers
128 views
How to solve equation involving binomial coefficient?
I'm reading this paper which says
If we have
$$
\binom n d p^{\binom d 2} = 1
$$
where $ 0 < p \le 1$, then
$$
d = 2 \log_bn - 2 \log_b \log_b n + 2 \log_b\left(\frac 1 2 e\right) + 1 + O(1)
...
1
vote
0answers
279 views
Observed information matrix is a consistent estimator of the expected information matrix?
I am trying to prove that the observed information matrix evaluated at the weakly consistent maximum likelihood estimator (MLE), is a weakly consistent estimator of the expected information matrix. ...
2
votes
2answers
1k views
Central Limit Theorem and sum of squared random variables
This is a two-part question.
Suppose I am drawing random variables $X_i\sim A$, $1\leq i \leq n$ where $A$ is a zero-mean, finite variance $\sigma_A^2$, symmetric probability distribution having ...
0
votes
2answers
135 views
Asymptotic probability: boys and girls in a line
We have $n$ people: $\alpha n$ are boys and $(1-\alpha)n$ are girls. They are standing in a line in a random order. We pick up one boy also at random.
What can one say about the probability that ...
