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Questions tagged [mathematical-statistics]

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

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p-vector and K-vector

I'm reading "The Elements of Statistical Learning" and early on there are references to p-vectors (page 10) and K-vectors (page 12). What exactly is meant by a p-vector and K-vector?
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2answers
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Is there a limit function in R?

Is there a 'limit' function in R? help(lim) or help(limit) weren't useful. And in general, is R suitable for mathematical ...
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3answers
747 views

Which test to find out best concentration (the one having maximum effect)?

Hi my apologies first, I'm a biologist and not so good in statistics. In my study I'm studying the effect of concentration of feed on growth of a certain specimen. I have with me the different ...
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1answer
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Choosing the right threshold for a biometric trait authentication system

I have a biometric authentication system that is using a person's gait to authenticate them. I extract features from gait, run it through a comparison versus a template and produce a similarity score (...
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2answers
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Calculate ROC curve for data

So, I have 16 trials in which I am trying to authenticate a person from a biometric trait using Hamming Distance. My threshold is set to 3.5. My data is below and only trial 1 is a True Positive: <...
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3answers
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How to use CDF and PDF statistics for analysis

This may be too much of a general question but I hope I can find help here. I am starting a RA job in my university and my topic will be related to Internet Traffic Analysis. I am fairly new to the ...
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4answers
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Who uses R with multicore, SNOW or CUDA package for resource intense computing?

Who of you in this forum uses ">R with the multicore, snow packages, or CUDA, so for advanced calculations that need more power than a workstation CPU? On which hardware do you compute these scripts? ...
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2answers
307 views

Sum of squares two ways, how are they connected?

The standard sum of squares as I know it is: $$ \sum(X-m)^2 $$ where $m$ is the mean. I ran into a different one which can be written two ways: $$ \sum(X^2) - \frac{(\sum X)^2}{n} = \sum(X^2) - m\sum ...
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14answers
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What is the most surprising characterization of the Gaussian (normal) distribution?

A standardized Gaussian distribution on $\mathbb{R}$ can be defined by giving explicitly its density: $$ \frac{1}{\sqrt{2\pi}}e^{-x^2/2}$$ or its characteristic function. As recalled in this ...
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4answers
505 views

Do third order asymptotics exist?

Most asymptotic results in statistics prove that as $n \rightarrow \infty$ an estimator (such as the MLE) converges to a normal distribution based on a second-order taylor expansion of the likelihood ...
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1answer
13k views

Regression Proof that the point of averages (x,y) lies on the estimated regression line

How do you show that the point of averages (x,y) lies on the estimated regression line?
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1answer
141 views

Large deviations proof question

Below is part of the proof of large deviations result. K is cumulant generating function. Can anyone explain how the last step follows? This is page 157 of McCullagh's "Tensor Methods in Statistics"
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Empirical relationship between mean, median and mode

For a unimodal distribution that is moderately skewed, we have the following empirical relationship between the mean, median and mode: $$ \text{(Mean - Mode)}\sim 3\,\text{(Mean - Median)} $$ How ...
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5answers
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Standard reference for classical mathematical statistics?

Can anyone recommend some books that are considered to be standard references for classical (frequentist) statistics? IE, fairly comprehensive, and also, been around for a while so that typos and ...
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2answers
334 views

How to prove the exponential expansion recursive form?

Consider the following exponential expansion form: $$ \exp\left[\sum_{k=1}^\infty \gamma_k x^k\right] = \sum_{j=0}^\infty\delta_j x^j $$ where $\gamma_k$'s are known, and $\delta_0=1$, $$\delta_{j+1}...
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2answers
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Why does the supremum of the Brownian bridge have the Kolmogorov–Smirnov distribution?

The Kolmogorov–Smirnov distribution is known from the Kolmogorov–Smirnov test. However, it is also the distribution of the supremum of the Brownian bridge. Since this is far from obvious (to me), I ...
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1answer
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Intuition for higher moments in circular statistics

In circular statistics, the expectation value of a random variable $Z$ with values on the circle $S$ is defined as $$ m_1(Z)=\int_S z P^Z(\theta)\textrm{d}\theta $$ (see wikipedia). This is a very ...
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3answers
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Non-trivial bound for $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$

How to find a non-trivial upper bound on $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$? A trivial bound is obtained for substituting $Z$ with $n$. A background on this ...
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14answers
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Simple algorithm for online outlier detection of a generic time series

I am working with a large amount of time series. These time series are basically network measurements coming every 10 minutes, and some of them are periodic (i.e. the bandwidth), while some other aren'...
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21answers
68k views

What's the difference between probability and statistics?

What's the difference between probability and statistics, and why are they studied together?
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19answers
7k views

Mathematical Statistics Videos

A question previously sought recommendations for textbooks on mathematical statistics Does anyone know of any good online video lectures on mathematical statistics? The closest that I've found are: ...
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6answers
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Motivation for Kolmogorov distance between distributions

There are many ways to measure how similar two probability distributions are. Among methods which are popular (in different circles) are: the Kolmogorov distance: the sup-distance between the ...
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Testing (and proving) the randomness of numbers [duplicate]

Possible Duplicate: Testing random variate generation algorithms What's a good way to test a series of numbers to see if they're random (or at least psuedo-random)? Is there a good statistical ...
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8answers
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What is meant by a “random variable”?

What do they mean when they say "random variable"?