# Questions tagged [mathematical-statistics]

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

4,074 questions
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### Matching Pursuit & Boosting: Exponential Convergence?

In the paper by Bühlmann BOOSTING FOR HIGH-DIMENSIONAL LINEAR MODELS, he introduces an algorithm, called componentwise linear least squares, and relates it to the Matching Pursuit algorithm by Mallat &...
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### Main differences (problems and mathematics) between traditional statistics and high dimensional statistics

High dimensional statistics seems to be hot nowadays. What are the main differences, in terms of questions and problems it tries to solve, as well as the mathematical tools used, between "traditional"...
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### Quantifying time series predictions

After building a time-series prediction model, Test Data: ...
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### Did Deborah Mayo refute Birnbaum's proof of the likelihood principle?

This is somewhat related to my previous question here: An example where the likelihood principle *really* matters? Apparently, Deborah Mayo published a paper in Statistical Science refuting Birnbaum'...
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### singularity at the origin of a particular function

what does it mean to say that a particular function is singular at the origin? e.g., it is said that the SCAD penalty is singular at the origin does not have continuous second order derivative. then ...
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### Survival Analysis - Relationship between CDF and survival function

I am trying to teach myself survival analysis and I followed this youtube video. The video states that given: $F_x(t) = \Pr[T_x \leq t ]$ is the future probability of the life for a person who has ...
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### Projection in AR model

I am currently reading the Brookwell and Davis Book and cuurently read about the PACF. On page 98 they derive the PACF for the AR(1) model $$X(t)=0.9X(t-1)+Z(t)$$ and say that the orthogonal ...
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### Possible to do some kind of statistical analysis without N?

So the thing is that I got some good data for my research project, but the problem is that the data I got only have percentages and standard errors, but no population (N). I would need to do some ...
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### Transform X to get Y such that Y has a Uniform(0,1) distribution

A random variable $X$ has the PDF $f_X(x) = \frac{x - 1}{2}, \ 1 < x < 3$ Find a monotone function $u(x)$ such that the variable $Y = u(X)$ has the distribution $Uniform(0,1)$.
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### Where is my mistake in this definition of Bayes Factor?

From "The Bayesian Choice" by Christian P. Robert. The definition of the Bayes factor is given to be the ratio of the posterior probabilities of the null and the alternative hypothesis over the ratio ...
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### Regression model when the dependent and independent variables show exponential distribution

As the Title suggests i am trying to figure out what would be the regression model to use when both the dependent and independent variables show an exponential distribution. Do I have to perform a ...
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### An example where the likelihood principle *really* matters?

Is there an example where two different defensible tests with proportional likelihoods would lead one to markedly different (and equally defensible) inferences, for instance, where the p-values are ...
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### How to prove the distribution of Generalised Instrumental Variables Estimator

$\hat { \beta } _ { GI V } = ( X ^ { \prime } Z ( Z ^ { \prime } Z ) ^ { - 1 } Z ^ { \prime } X ) ^ { - 1 } X ^ { \prime } Z ( Z ^ { \prime } Z ) ^ { - 1 } Z^ { \prime }y\hspace{35pt}(a)$ $(a)$ is ...
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### Does this correlation make sense?

I'm trying to work on a ML project and I have a dataset and I'm trying to see if there is a correlation between some of the features in my dataset. The dataset contains inspection notes for car parts ...
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### need explanation about the exponent parameter s in zipf distribution

I need to model the popularity of some requested files from a library with Zipf distribution and I want to simulate it in MATLAB. I don't know what's the effect of parameter s on my result. for ...