# Questions tagged [mathematical-statistics]

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

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### Finding variance in restricted row in long process [closed]

I have a data imported from an excel file. I want to find variance of each 13 rows such that firtly calculate the variance of row [1-13] (1 and 13 inclusive) , after that row [2-14] , after that row[3-...
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### Strong Law of Large Numbers for bootstrapping: Proving bootstrap sample mean converges a.s. to mean

Setup Let $X_1, X_2, \dots$ be an i.i.d. sequence of random variables with the common distribution function $F(\cdot) := \mathbb P(X_1 \leq \cdot)$ and finite first moment $\mathbb E[X_1] <\infty$. ...
12 views

### Proof Maximum likelihood Hypergeometric model [closed]

Could somebody explain me how to infer in the hyper geometric model, and show the proof to obtain rigorously the maximum likelihood estimator in this model ?
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### Expected value of log-likelihood and KL divergence

Background: Let $x_t = Ax_{t-1} + w_t$ be a discrete linear time invariant system where: $x_t \in \mathbb{R}^d$ for all time samples $t$ corresponds to the state vector $A\in \mathbb{R}^{d\times d}$ ...
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### consistency of mle of double exponential distribution ( not advanced)

Let $y_i\sim DE(\mu, \sigma),$ $i=1,2,...,n, \ i.i.d.$ Where DE represents the double exponential distribution. The the MLE of \sigma is: $\hat\sigma = \frac{1}{n} \sum_{i=1}^{n}|y_i-med(y_i)|$, ...
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### Finding a statistical method to summarizes set of points [closed]

I want you to help me find a statistical method that summarizes these points in a single point. The idea from each of these points is to find how close they are to one. Therefore, I would just like to ...
40 views

### Variance of the median

For large $N$ the sample median is approximately normally distributed with mean $μ$ and variance $π/2N$. The efficiency for large $N$ is thus $2/π≈0.64$ Can somebody explain this for me? Where does ...
34 views

### Standard deviation of population and sample [closed]

I have a value of population's standard deviation (say σ) and I have sample of size N and SD of sample (say s). Population and sample supposed to be normally-distributed. Using χ² distribution I can ...
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### Statistics question [closed]

An athletic teams consists of 2 Level 1 students, 5 Level 2 students and 3 Level 3 students. The team members are ranked according to their performance after a race. Assuming no 2 team members run the ...
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### How to optimize a function with respect to a distribution, in the context of variational inference

Context: I am learning about variational inference. The reference I am following is linked at the end of this post. Goal: I want to learn how a marginal variational distribution $q_k$ is optimal in ...
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### Derive the distribution of the fraction ${\sum{x_i}}\Big/{\sqrt{\sum{x_i^2}}}$ [closed]

Suppose ${X_i}$ follows the standard normal distributon N(0,1), what is the distribution of $\frac{\sum{x_i}}{\sqrt{\sum{x_i^2}}}$
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### How to check for the accuracy of prediction

I am doing a personal project to see how well does FIFA potential player stats predict the actual overall stat after 3 years. Meaning, if a player has a potential of 85 in 2015, how accurate should I ...