# Tagged Questions

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

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### Implicit estimator, it's variance and expectaion

Denote with $V_j$ the firm's value of $j$-th firm. We will speak of default, if the firm's value falls below predefined barrier $c \in \mathbb{R}$. The random variable $L_j$ will indicate, if $j$-th ...
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### Evaluation of a binary classifier in regards of rounding, taking average scores

I'm using scikit-learn to evaluate a binary classifier: There are 2 Methods to get the Precision, Recall and F1 scores: 1.classification_report: ...
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### Is it always true that $P(X| Y \text{ OR } Z) \le P(X|Y)$?

Consider the following argument: If $(X| Y \ \text{OR} \ Z)$ is true, $(X| Y)$ must be true. For example, if $f(t)=10$ when $t=1$ or $\ t=0$ is true, then $f(t)=10$ when $t=1$ must be true ...
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### Does a random sample size produce a larger or smaller variance than a fixed sample size?

If you run two identical samples with the exception of the sample size where in both cases E(n)=1000, but in one the variance is 0 (ie. fixed sample size of 1000) and the other has non-zero variance, ...
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### compare the similarity of two cluster results using igraph

i am comparing the results of two clusters using igraph, such as What is the intuition behind the variation of information (VI) metric for cluster validation? I see there were consistency for all ...
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### Geometry of Rejection regions for tests (NP lemma, Karl-Rubin, UMPU, LMP, etc)?

The Neyman-Pearson lemma, the Karlin-Rubin theorem, and the other for UMPU tests for the exponential family, etc. They all define a most powerful Rejection Region (RR), in a certain class of tests. I ...
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### A uniformly optimal statistical procedure? an exercise from The Bayesian Choice

The previous exercise is from the book 'The Bayesian Choice', page 87. What does the author mean by uniformly optimal stat. procedure? This exercise refers to a Decision theory chapter, in a section ...
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### Comparing relative error measures

So I have a list of actual values and two models to predict these values. Evaluating the predictions gives me a relative (absolute) error of 50% percent for the first and 25% for the seconds. I'm ...
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### Whitening transform for the case of two stochastic processes

The classic whitening transform allows us to find a linear transformation for a given random process X, yielding a new process Xw with a unity Covariance matrix. Given an extended problem with two ...
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### Objects and properties classification

I have a list of properties and objects: ...
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### Prediction Algorithms in Statistics

Here it is what I'm looking for: Having a random variable, with an unknown distribution of its values, is there any smart algorithm that can predict the next value of the variable based on n samples ...
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### Calculating probability of an event involving two normally distributed random variables

I have two normally distributed, independent random variables $S^{(1)}$ and $S^{(2)}$: $$S^{(1)} \sim \mathcal{N}(\mu_1, \sigma_1^2),\ S^{(2)} \sim \mathcal{N}(\mu_2, \sigma_2^2)$$ Given two positive ...
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### What does “Borel space”, unqualified, refer to? [migrated]

For examples of use, Google "in Borel space", without the quotes. I'm thinking it means either ℝ equipped with its Borel σ-algebra, or to Borel spaces in general (that is, topological spaces with a σ-...
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### Amplitude of Sine wave [migrated]

How can I alter amplitude of a sine wave, such that it is in the range of [-1,30]? $y = A\sin(\theta t + \phi)$. I want $A$ to be 30 and $-A$ to be -1.
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### By which ways can we, in principle, evaluate whether a model succeeded in generalizing?

A disclaimer: By using an informal term such as "generalize", I am aware I am getting close to philosophical territory, and that my question could be seen as unsuitable for CV. I will do my best ...
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### A measure for sustained activity (dispersion)

I need a numeric measure that determines a level of sustained activity. Let me describe a situation in which this could be useful. Imagine that you have a Twitter feed in which you are tracking words ...
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### Order of ARMA models

Why we usually do not exceed ARMA(5,5) models in practice? Is there any mathematical justification for this?