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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an application of nth moment of Poisson distribution with stirling number

I was reading the paper on arixv. I was confused the equation of nth moment of Poisson distribution. The detail and partial paper as follow: ... For large N, this connection probability takes ...
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How sensitive is ML-estimation of the expected value if the covariance matrix is not correct?

Suppose, we have a random variable $Y \sim \mathrm{N}\left( Ax, \, \Sigma \right)$ and realisations $y$. I would like to estimate $x$, the parameter of the expected value. The loglikelihood function ...
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Central Limit Like theorem for the distribution of F-statistics on all possible partitions?

I'd be happy for simply a reference or even search terms as I feel like this has to be known*. Suppose we have a known probability distribution $X$ and a fixed integer $n$. I am interested in the ...
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Lower bounds on Kullback-Leibler divergence

This was originally a question on Cross Validated. Are there any (nontrivial) lower bounds on the Kullback-Leibler divergence $KL(f\Vert g)$ between two measures / densities? Informally, I am ...
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Extremal Covariance Duality

Given real vectors $v$ and $r$ of the same size, what are the following? $\inf\{v'R^{-1}v ~ \colon ~ R>0 \, , \, \text{diag}(R)= r\}$ $\sup\{v'Rv ~ \colon ~ R>0\, , \, \text{diag}(R)= r\}$ ...
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Rank of Hadamard product with random matrices

I do research in statistics and am not sure whether the following is considered research level or not in mathematics. If it isn't, I'm happy because that means the answer is probably known and I can ...
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Upper bound total variation by Wasserstein distance for continuous distance

I am reading the survey of the relationships between metrics of distributions (see https://arxiv.org/pdf/math/0209021.pdf for the paper). The general results show that for general distributions, we ...
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Multivariate normal concentration

If $X\sim N(0,\Sigma)$ for some $d$-dimensional normal distribution, then $X = \Sigma^{1/2} Z$ where $Z\sim (0,I)$. How to compute the following quantity?  \operatorname{var} (X^T X) = \...
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Confidence intervals for the endpoints of the uniform distribution

Consider $n$ iid observations $X_1,X_2,\dots ,X_n$ from a $Uniform(a,b)$ distribution, where $a$ and $b$ are both unknown. How do we construct a joint confidence interval for $(a,b)$? I would prefer ...
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Expand the pdf of Wishart distribution into power series via orthogonal polynomials

In the univariate case ($\chi^2$ distribution), I know we can expand the pdf into power series of the variance $\sigma^2$ with Laguerre polynomials. Indeed, since the Laguerre polynomials are related ...
Let $W_u, 0\leq u \leq t$ be Brownian motion. Let $m_t= min_{0\leq u\leq t} W_u$ and $M_t = max_{0 \leq u \leq t} W_u$. The fact that $(M_t , W_t)$ is absolutely continuous with respect to Lebesgue ...