# 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.

1,517 questions
Filter by
Sorted by
Tagged with
5 views

49 views

73 views

94 views

### Convergence of quadratic form $y^T Q y$ where $y$ is a random iid sequence of length $n$ and $Q$ is an $n \times n$ random matrix independent of $y$

For each positive integer, let $Q_n=(q_{i,j})_{i,j \in [n]}$ be a random $n \times n$ psd matrix. In the limit $n \to \infty$, suppose the eigenvalues of this sequence of matrices are uniformly ...
67 views

### Probability to cross an envelopp for 1D random walk?

Imagine we have an evolving sequence composed of 1 and -1 (ex: -1-11-111...) where the probability to get -1 or 1 is 1/2. n is the lengh of my sequence. I can make an analogy with random walk: let ...
71 views

41 views

### Bootstrap-$t$ confidence intervals

I'm writing a dissertation about bootstrap methods and the main book I'm using is Efron, B., & Tibshirani, R.J. (1994), An Introduction to the Bootstrap (1st ed.), Chapman and Hall/CRC. Now I need ...
79 views

### Are the first 4 statistical moments independent? [closed]

Are the first 4 statistical moments independent? Is there a mathematical demonstration that can show independence one from each other? Can the value of one moment influence the value of another? If so,...
21 views

### Empirical covering number bounds of functions in rkhs ball

In this paper https://arxiv.org/pdf/1905.11882.pdf, the authors rely on showing the optimal "potential" functions lie in a set with a bounded Holder norm. They're able to show specific ...
99 views

### Are there any function spaces with bounded gradients?

Are there any known function spaces where the gradients are uniformly bounded? For a problem I’m working on, I’ve been able to show my functions are bounded in a ball within an RKHS (reproducing ...
26 views

68 views

### sub-exponential type upper bound on the Poisson probability

I posted this question on Math Stack Exchange, though I'm not satisfied with the answer I received. Question: For a Poisson random variable $Z$ with the parameter $\lambda,\,$ what would be a good ...
71 views

### Testing uniformity for continuous probability distributions

Suppose I can sample from a random variable $X$ which is distributed on a compact interval, say, $[0,1]$. Fix a distance measure between distributions, say total variation. Let $\epsilon\in(0,1)$. How ...
56 views

### On estimating Covariance between a random variable and its non-linear transform

Let $X$ be a random variable taking values on the real line. Let $R(X) = max\{0, X\}$. Is it true that the covariance $Cov[X, R(X)] \ge 0$ irrespective of the distribution of $X$? Many experiments, as ...
71 views

### Expected value of Tukey’s half-space depth for log-concave measures

Let ${\mathbb P}$ be a probability measure in ${\mathbb R}^n$. Let $x\in{\mathbb R}^n$ be an arbitrary point. Let ${\mathbb H}_x$ be the set of halfspaces of ${\mathbb R}^n$ containing $x$. Let \begin{...
128 views

27 views

128 views

### Expectation of product of random matrices

Let $X$ and $Y$ be independent random symmetric matrices. What can one say about $\mathbb{E} [X Y X Y]$ or $\mathrm{trace} \mathbb{E} [X Y X Y]$ in terms of properties of $X$ and $Y$? In particular, ...
184 views

### High-probability lower bound for norm of least squares solution when both design matrix $X$ and response vector $y$ are random (and independent)

Let $n,d \to \infty$ with $n/d \to \gamma \in (0,\infty)$. Let $X$ be a random $n \times d$ matrix independent rows uniformly distributed on the the unit-sphere in $\mathbb R^d$ and let $y$ be a ...
102 views

### A basic property of maximal correlation

Let $𝑋$ and $𝑌$ be random variables. Then the maximal correlation $\rho_{m}(X;Y)$ is defined as: $$\rho_{m}(X;Y):=\max_{f,g}\mathbb{E}[f(X)g(Y)],$$ where the maximization is taken over real-valued ...
55 views

### Normalizing constants preserve metric entropy

Suppose $\mathcal{F}=\left\{f\in L^2([a,b]): 0<\underline{c}\leq f\leq\overline{c} \right\}$. Consider the following transformation \tilde{\mathcal{F}} := \left\{\frac{f}{\int f d\mu}: f\in \...