Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [mathematical-statistics]

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

Mathematical statistics is the study of statistics from a mathematical point of view, concerned with formal definitions and general results.

References

The following threads contain extensive references for studying mathematical statistics:

The following journals are dedicated to research in mathematical statistics:

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What's the difference between variance and standard deviation?

I was wondering what the difference between the variance and the standard deviation is. If you calculate the two values, it is clear that you get the standard deviation out of the variance, but what does that mean in terms of the distribution you…
Le Max
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Bottom to top explanation of the Mahalanobis distance?

I'm studying pattern recognition and statistics and almost every book I open on the subject I bump into the concept of Mahalanobis distance. The books give sort of intuitive explanations, but still not good enough ones for me to actually really…
jjepsuomi
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What's the difference between probability and statistics?

What's the difference between probability and statistics, and why are they studied together?
hslc
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Why does the Cauchy distribution have no mean?

From the distribution density function we could identify a mean (=0) for Cauchy distribution just like the graph below shows. But why do we say Cauchy distribution has no mean?
Flying pig
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Numerical example to understand Expectation-Maximization

I am trying to get a good grasp on the EM algorithm, to be able to implement and use it. I spent a full day reading the theory and a paper where EM is used to track an aircraft using the position information coming from a radar. Honestly, I don't…
arjsgh21
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Maximum Likelihood Estimation (MLE) in layman terms

Could anyone explain to me in detail about maximum likelihood estimation (MLE) in layman's terms? I would like to know the underlying concept before going into mathematical derivation or equation.
StatsUser
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Validation Error less than training error?

I found two questions here and here about this issue but there is no obvious answer or explanation yet.I enforce the same problem where the validation error is less than training error in my Convolution Neural Network. What does that mean?
Bido
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104
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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't (i.e. the amount of routing traffic). I would…
gianluca
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How does the reparameterization trick for VAEs work and why is it important?

How does the reparameterization trick for variational autoencoders (VAE) work? Is there an intuitive and easy explanation without simplifying the underlying math? And why do we need the 'trick'?
David Dao
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If mean is so sensitive, why use it in the first place?

It is a known fact that median is resistant to outliers. If that is the case, when and why would we use the mean in the first place? One thing I can think of perhaps is to understand the presence of outliers i.e. if the median is far from the mean,…
Legend
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Who Are The Bayesians?

As one becomes interested in statistics, the dichotomy "Frequentist" vs. "Bayesian" soon becomes commonplace (and who hasn't read Nate Silver's The Signal and the Noise, anyway?). In talks and introductory courses, the point of view is…
Antoni Parellada
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What is meant by a "random variable"?

What do they mean when they say "random variable"?
Baltimark
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Mutual information versus correlation

Why and when we should use Mutual Information over statistical correlation measurements such as "Pearson", "spearman", or "Kendall's tau" ?
SaZa
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Famous statistical wins and horror stories for teaching purposes

I am designing a one year program in data analysis with a local community college. The program aims to prepare students to handle basic tasks in data analysis, visualization and summarization, advanced Excel skills and R programming. I would like…
Placidia
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Central limit theorem for sample medians

If I calculate the median of a sufficiently large number of observations drawn from the same distribution, does the central limit theorem state that the distribution of medians will approximate a normal distribution? My understanding is that this is…
user1728853
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