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Results tagged with st.statistics
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user 28161
Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.
4
votes
1
answer
1k
views
Quantile convergence
Let $X^1,\dots,X^n$ be a sample of (not necessarily iid) random variables and denote
$$F^n(x)=\frac{1}{n}\sum_{i=1}^n \mathbf 1_{X^i\leq x}$$
the empirical distribution function. Suppose that we know …
- 293
1
vote
0
answers
54
views
Minimal rectangular confidence regions
For a given multivariate pdf $f$ (mainly the gaussian one) I'm looking to compute a minimal rectangular confidence region for a given level $\alpha$. For example, I would like to solve problems of the …
- 293
0
votes
Accepted
Estimate on gaussian distribution
Based on Carlo's contribution, after short manipulations I got to the answer
$$f(M)=\left(1-\exp\left(-\frac{M^2}{d^2 \|C\|^2}\right)\right)^d,$$
for the full rank case, where $\|C\|=\max |C_{ij}|$ an …
- 293
4
votes
2
answers
325
views
Estimate on gaussian distribution
Let X be an $\mathbb R^d$-valued random variable with distribution $N_d(0,\Sigma)$. I'm looking for a function $f$ such that
$$P(|X_1|\leq M, |X_2|\leq M,\dots, |X_d|\leq M)\geq f(M),$$
and such that …
- 293