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# Questions tagged [mathematical-statistics]

Mathematical theory of statistics, concerned with formal definitions and general results.

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### Monte carlo method and Convergence in Distribution

Monte Carlo method, from what I could gather, allows one to obtain observations/draws from a possibly unknown statistical distribution. Let's say $T(X)\sim F$, where $T$ is a statistic, $X$ is a ...
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### Does MCMC method can be used to calculate the mean and variance of the distribution of random variable functions?

I am not professional in Probability & Statisticsin, in order to clearly describe my problem, please be patient of the long introduction.THANKS! Background of my question Assume I have several ...
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### Finding the asymptotic distribution of $\frac{1}{n+k}\sum_{i=1}^{n}X_i$

Let $(X_1,X_2,...,X_n)$ be a random sample from a population distribution with $E(X_i)=\mu$ and $Var(X_i) =\sigma^2$ for all $i$ find the asymptotic distribution of $T= \frac{1}{n+k}\sum_{i=1}^{n}X_i$...
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### Asymptotic Distribution of the Wald Test Statistic

I am trying to understand the asymptotic distribution of the Wald test statistic, specifically under the alternative hypothesis which I've found little reference to. For clarity, the binary ...
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I'm working through Convolutional Neural Network paper here on adversarial learning and I'm having trouble with the derivative proof of adversarial logistic regression. The correct answer presented (...
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### Limiting distribution of $\frac{\bar{x}-p}{\frac{pq}{n}}$ from mean of $Bin(1,n)$?

I found some difficulties in here. We know that if $X$ has Binomial distribution with $1$ trial and $p$ success, or what we called $X$~$Bin(1,p)$, we have $\mu=p$ and $\sigma^2=p(1-p)=pq$. From that, ...
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### Markov model parameter concentration and Fisher Information Matrix

For iid data, the posterior on the parameter $$p(\theta \mid x_{0:T}) = \prod_{t=0}^T p(x_t \mid \theta) p(\theta)$$ is known to become independent of the prior which is the Bernstein-von Mises ...
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### Mahalanobis distance for highly multivariate random variable

I have to compute the Mahalanobis distance for a $10^6$ dimensional multivariate random variable. What is the best (and fastest) way to do this? I am currently taking cholesky decomposition of the ...
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### Confidence bounds on mean of a limited normal distribution

Suppose we are sampling from an underlying normal distribution with mean $\mu$ and variance $\sigma^2$, i.e $\mathcal{N}(\mu, \sigma^2)$. However, whenever we find a sample value that is greater than ...