# 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
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### Why the autoregressive process to generate random time series?

in order to test some forecasting methods, I desire to generate random time series. I'm about to use the AR(1) model: $X_k=\alpha X_{k-1}+ \epsilon_k$ With eventually: $\alpha>1$ How can I ...
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### Empirically random, quickly multiplicable matrices

I have encountered a need for fast computation of a transformation $Ax$ where $A\in \mathbb{C}^{K\times N},\ K\sim 10^7,\ N\sim 10^3$ is designed, and $x\in \mathbb{C}^N$ has iid $\mathcal{CN}(0,1)$ ...
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### Rate of convergence of probabilities under Wasserstein convergence of measures?

Suppose $\mu=\sum_{i=1}^k p_i\delta_{x_i}$ and $\mu'=\sum_{i=1}^k p_i'\delta_{x_i'}$ are two atomic probability measures. Let $W_r(\mu,\mu')$ be the Wasserstein distance between $\mu$ and $\mu'$. Are ...
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Let $P$ be a probability measure and $f$ be some probability density function (not necessarily related to $P$). Consider the function $$L(X_1,\ldots,X_n) =\frac1n\sum_{i=1}^n\log f(X_i), \quad X_i\... 0answers 80 views ### Full-rank factorization property of integer-valued matrices \newcommand{\al}{\alpha} \newcommand{\de}{\delta} \newcommand{\De}{\Delta} \newcommand{\ep}{\varepsilon} \newcommand{\ga}{\gamma} \newcommand{\Ga}{\Gamma} \newcommand{\la}{\lambda} \newcommand{\Si}{\... 1answer 74 views ### Improved estimates of n quantities via n measurements \newcommand{\de}{\delta} \newcommand{\De}{\Delta} \newcommand{\ep}{\epsilon} \newcommand{\ga}{\gamma} \newcommand{\Ga}{\Gamma} \newcommand{\la}{\lambda} \newcommand{\si}{\sigma} \newcommand{\Si}{\... 1answer 70 views ### Optimal linear measurement operator Let x\in R^n be an unknown vector. Suppose I am allowed to choose any A\in R^{m\times n}, under the constraint that each row of A has \ell_2 norm at most 1. Then I carry out a "measurement", ... 1answer 452 views ### Mean and Variance of maximum of random variables Given a set of random variables x_1,x_2,...,x_n, and we know their means and variances (\mu_1,\sigma_1),(\mu_2,\sigma_2),...,(\mu_n,\sigma_n). How to compute mean and variance of the maximum ... 1answer 75 views ### Distribution of largest entry in a random vector If we have a random unit vector on \mathbb{C}^n, drawn from the Fubini-Study metric, the marginal distribution of the squared absolute values of each of the coefficients in the vector is given by a ... 0answers 35 views ### Control the variance of some coincidence statistic Let X = X_1, \cdots, X_m \sim D_d a sample of size m from a [d]-supported distribution. Let$$K_1 = K_1(X_1, \cdots, X_m) = \sum_{i = 1}^{d} \unicode{x1D7D9}\{B_i = 1\}$$with$$B_i = B_i(X_1, ...
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This might sound trivial or a simple misunderstanding, but please bear with me as I'm not a Math major. I want to investigate some aspects of PCA in homogeneous directions and needed simple ...
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### Are there any non-asymptotic bounds for the minimum empirical risk vs theoretical risk?

I'm trying to see if there's any bounds on the difference between $f_{ERM}$ and $f^{*}$. For now, define $\mathcal{F}$ to be a function class. Let $P$ be a probability measure and $\hat{P_n}$ be the ...
Suppose that there is an urn containing $n$ different coupons, from which $m$ coupons are being collected, equally likely, with replacement. Let $C(m)$ be the whole set of the $m$ collected coupons. ...