Questions tagged [st.statistics]

Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

1,206 questions
52 views

207 views

How to simulate random paths of a non-homogeneous continuous-time Markov process with discrete state space for a given infinitesimal generator matrix?

Let $X=(X_{t},\,t \in T)$ be a non-homogeneous, continuous time Markov process with a finite state space $S=\{1,...,K\}$. Let $\alpha_{i,j}(t)$ be the hazard rates of some $\varGamma$-distributed ...
19 views

Standard normal variable times an independent random variable [closed]

Hello I am unsure about the distribution of a variable. If X~N(0,1) and P[V=1]=P[V=-1]=0.5 Show that the distribution of VX is also standard normal. I understand that E[V]=0 and Var[V]=1 but I'm ...
16 views

Standardising a score of values help [closed]

I am working on developing on a standardised score from a number of scores. The values will be ranging from large to small of each score and I am trying to develop a way of proportionally measuring ...
172 views

Are Linear Maps resistant to Noise?

Let's assume I have a $m \times m$ matrix $M$ with Frobenius norm $1$ and a unit vector $x \in S^{m-1}$. I also have a second $m \times m$ matrix $M^*$ which is obtained from the first one plus some ...
19 views

Parametric statistics: how to estimate the supremum of a set of parameters from a random sample

I would like to ask a question on how to estimate the supremum norm of a set of parameters in the following setting. I appreciate any pointer or suggestion. Thanks. Question: Suppose we have $m$ ...
509 views

Random Walks on high dimensional spaces

I've read on a paper that, in the two dimensional case, if you start from the origin and take steps of length one in arbitrary directions (uniformely on the unit sphere $S^1$, not left-right-up-down), ...
165 views

9k views

What's an efficient way to calculate covariance for a large data set?

What is the best algorithm for computing covariance that would be accurate for a large number of values like 100,000 or more?
16 views

Non-asymptotic tail-bounds for Hotelling $T^2$ statistic

Let $X_1,\ldots,X_n$ be an i.i.d sample from a distribution on $\mathbb R^p$ with mean $\mu = 0 \in \mathbb R^p$ and $p$-by-$p$ covariance matrix $\Sigma$ of rank $r \le p$. Consider the centered ...
100 views

A problem related to the comparison of two integer-valued random variables

Consider an urn containing red, blue and green balls (the situation is the same illustrated in this post). Let $X$ be the non-negative, integer-valued random variable defined as the number of trials (...
456 views

Practical bounds for the Wasserstein distance in 2 dimensions

Let $X_1,\dots,X_n$ be a set of independent samples of a distribution $\mu$ on the unit square, let $\hat\mu_n$ be the empirical distribution on the points $X_1,\dots,X_n$, and let $W_1(\mu,\hat\mu_n)$...
111 views

Expected distance of nearest matching pair in the game of pairs

Recently I was playing several rounds of the game of pairs with my children. I was surprised that almost every time, one matching pair was adjacent (either next to each other in a row, or vertically). ...
19 views

Practical statistics for queueing networks

There is a theory for queueing networks where we postulate some nicely behaving base distributions of arrival processes and service processes and then calculate the behaviour of the system. Now, in ...
87 views

Minimum number of support vectors? [closed]

I'm learning SVM and its written everywhere that the minimal number of support vectors is 2? But I couldn't find any formal proofs of that. Why cant there be less than 2 support vectors? Can somebody ...
44 views

Does lattice mod preserve direction?

For high enough dimension $n$ there are lattices $L_n$ in $\mathbb{R}^n$ whose Voronoi partition's base regions encompass all but a negligible proportion of a $(1-\varepsilon)$-ball, and also nearly ...
69 views

40 views

Characterisation of a superset of the simplex

Does there exist a nice description of the following set: A:=\left\lbrace x\in\mathbb{R}^{n}\ \colon\ 0< x_{i}-\bar{x}+\frac{1}{n}< 1\ \text{for} \ i=1,\dots,n\right\rbrace, \...
82 views

Non-asymptotic tail bounds for $D_{\text{Hellinger}}(P\|\hat{P}_N)$

Let P be a distribution on a finite set of size $k$ and let $\hat{P}_N=(N_1/N,\ldots,N_k/N)$ be the empirical distribution (frequencies) from a samples of size $N$. Consider the Hellinger distance ...
Ideally what I am looking for two random variables, $X$ and $Y$ (if one is positive then that's even better) such that $Z=X\cdot Y\sim\mathcal{N}(0,1)$ where $X,Y$ are some distributions I can ...