# Questions tagged [mathematical-statistics]

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

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### In elastic net regularisation, will dividing the OLS term the number of observations cause misleading results when cross-validating?

Two formulations of the elastic net regression function Consider sklearn's implementation of elastic net regularisation. From the docs, it works by minimising the ...
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1 vote
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### Issue with bounded in probability

I have tried to prove the following problem that I read in the lecture and it seems not transparent to me. Suppose that $Y_{i}$ be independent random variables (with $i=1,2,3,...$). Each has the ...
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### Bounds on the conditional variance of a truncated binomial

I have a binomial variable $R$ drawn from $binom(N, p)$, and I'm interested in the variance of $R$, given $R \ge Q$. The pmf of this variable $R^*$ is $$\phi_{R^*}(l) = \frac{\phi(l, N, p)}{P}$$ ...
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### How can I calculate Posterior Distribution, analytically with given information?

The image below shows that the posterior distribution is as follows with given information: I wonder how the posterior has been calculated, analytically.
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1 vote
41 views

### Conditioning of join gaussian over a line

I need to compute the conditional probability of bivariate normal distribution over a line. Let's suppose that X and Y both are normal distributions and that they are independent. Let's suppose that ...
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### Gauss-Markov with $p>n$

Let $p$ be the number of parameters in a linear regression model, let $n$ be the number of observations, and let $p>n$. $$\mathbb E[Y\vert X] = \beta_0 +\beta_1X_1 +...+\beta_pX_p$$ Does the Gauss-...
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1 vote
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### Are there possibilities to determine 95% confidence interval for right skewed data?

The dataset that I'm using for my thesis is right skewed. It is about lead times (days) I tried log10 transforming it in SPSS but it still does not meet the requirement p>0,05 (Shapiro-wilk). So ...
51 views

### What is the conditional expectation of two random Poisson variables?

Say I have two random variables $Z^{p}_{i} \mid Y^{p}_{i} \sim \text{Poisson} \left(t^{p}_{i}Y^{p}_{i}\right)$ and $Z^{q}_{i} \mid Y^{q}_{i} \sim \text{Poisson} \left(t^{q}_{i}Y^{q}_{i}\right)$ for ...
27 views

### Comparing current and new version of Autoencoder

I am building an LSTM Autoencoder (unsupervised model) to detect anomalies in a time series dataset. The input is telemetry data from routers and I want to detect anomalies in the throughout of ...
34 views

### two sample t-test for non-normal population

I assume this question has been beaten to death and thus I am just looking for a reference which goes through the details. Assuming all populations we deal with have finite means and variances (even ...
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### What is my best option to evaluate a predictive (or proxy) variable?

I have a list of thunder flashes, and I'm trying to find if a meteorological variable (CAPE) is a good predictable variable (or proxy) for theses flashes. In my thoughts, I want to evaluate this proxy ...
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### How to generate a general trend from hundreds of time-series data

I have hundreds of time-series data from individual experiments[2] with a similar trend that reading rises as time goes by (evaluated by my naked eyes). So what statistical tools should I use to ...
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1 vote
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### how to find standard deviation of sampling distribution without knowing population parameter σ

Standard deviation of sampling distribution is given as σ/sqrt(n). But usually the population parameter σ will be unknown. In that case, how do we calcuate the standard deviation of sampling ...
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