# Questions tagged [mathematical-statistics]

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

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### Why is MSE used in cross validation when selecting optimum number of variables in model?

I'm currently looking through An Introduction to Statistical Learning by Gareth James, more specfically Chapter 6. It discusses ways to select the optimal number of variables in a model using methods ...
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### Does anyone know which book this pdf is from?

Does anyone know which book this pdf is from?
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### Question about calculating confidence intervals

I am reading about confidence intervals and got stuck with this example from L. Wasserman's book titled "All of Statistics". Could anybody explain why PQ(Īø ā C) = 3/4 in this example? Below is the ...
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### Is normalizing/standardizing features and target separately a good method?

Suppose I scaled the features and target by creating separate objects, like this ...
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### Bayes Classification vs Naive Bayes Classification

Generally, known that Bayes Classifier is optimal for the probability of error. But when I did some experiments: First Case: I have 2 classes data and their covariance matrices correlated in this ...
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### Probability of failure set

I want to prove the following theorem, which in general allows us to compute the probability of a certain set even if it contains no observations (which is all too common in extreme value analysis of ...
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### Finding quantiles of scalar non-decreasing function of two independent variables

Let $X_1 \sim exp \circ N(\mu_1, \sigma_1)$ and $X_2 \sim exp \circ N(\mu_2, \sigma_2)$ be two independent lognormal distributions, and $f:R^2\to R$ such that $f$ is non-decreasing on both arguments. ...
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### Risk of a learner as random variable

Assume the learner $h: X \to Y$ where $X \times Y$ with joint probability distribution $P_{X,Y}$ and assume a loss function $L$. Then the risk of $h$ associated to $L$ (and $P_{X,Y}$) is defined by ...
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### Would a z test be ok in this situation

I would like to know if I am doing this question correctly. The data I am using is from http://www.kaggle.com/mohansacharya/graduate-admissions. What I would like to do is, estimate the population ...
Suppose we are interested in the expectation of a test function $f(X)$ with respect to target distribution $\pi(X) \propto \gamma(X)$ using importance sampling with proposal distribution $q(X)$ with \$...