Questions tagged [mathematical-statistics]
Mathematical theory of statistics, concerned with formal definitions and general results.
8,006
questions
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Can an outcome variable be used twice in the same model?
When is it appropriate to use the same outcome variable in two likelihoods in the same model framework?
Here is a specific example:
...
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Convert Multivariate PDF to Anomaly based Risk Score on scale 0 to 1
I have defined a multi-variate normal distribution over a number of risk factors.
Currently the PDF over the risk factor observations ranges from infinitesimally values to a maximum of ~2.1.
While the ...
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Prove that variance of log Exp is greater than variance of Exp log
In the context of variational inference, we move from estimating the gradient of:
$\log E_{q \sim Q(z|x)} [ \frac{p(z,x)}{q(z|x)} ]$
to:
$E_{q \sim Q(z|x)} [ \log \frac{p(z,x)}{q(z|x)} ]$, which is ...
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1
answer
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Is the Sufficiency Principle an axiom?
Sufficiency Principle as defined in Casella:
Where Sufficient Statistic is defined as:
Question: Is the Sufficiency Principle an axiom?
My thoughts and research so far:
I'm uncertain if the ...
- 263
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Mathematical Introduction to Theory of Time Series Analysis
Assume that the reader has strong background in stochastic calculus (including and beyond continuous time stochastic processes like martingales and Markov chains and others, the construction of Levy ...
4
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2
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References to learn « Real and Functional Analysis for Statisticians »
I’m looking for a kind of book which gives the elements of Real Analysis for Mathematical Statistics and Econometric Theory, etc.
I’m planning to work with the 3 following textbooks on advanced ...
6
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1
answer
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What is the formula for the conditional inverse function for the Ali-Mikhail-Haq and the Farlie-Gumbel-Morgenstern Copulas?
I am trying to do a Monte Carlo simulation and want to define a function for the conditional inverse function for the the Ali-Mikhail-Haq and the Farlie-Gumbel-Morgenstern Copula. Here is an example ...
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Creating double sampling plans [closed]
I am trying to create double sampling plans. The product has to meet a reliability of at least 90% with 95% confidence. Assuming binomial distribution, I can create a single sampling plan by testing ...
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1
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Does $f : p_\theta\mapsto p_{T\,\mid\,\theta}$ being injective imply statistic $T $ is sufficient?
Wikipedia says
... consider the map $f:p_{\theta }\mapsto p_{T\,\mid\, \theta }$ which takes each distribution on model parameter $\theta$ to its induced distribution on statistic $𝑇$. The ...
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1
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How can I prove monotonicity of slope MLE in EIV regression model?
I'm trying to figure out Casella and Berger Exercise 12.4(c), regarding monotonicity of the maximum likelihood estimator of the slope of an errors-in-variables regression model. The goal is to show ...
- 11
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Reference request for the existence of minimal sufficient statistics
I'd like a recent paper or book that shows in what conditions we can guarantee the existence of a minimal sufficient statistic.
I know the paper "Sufficiency and Statistical Decision Functions&...
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77
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Rank probabilities for dependent data
It is well known that for iid sample $X_1, \dots, X_T$ rank probabilities are uniform over $1, \dots, T$. In other words, fixing $1 \le i_0 \le T$, probability of $X_{i_0}$ having rank $k$ (i.e., $X_{...
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What is the terminology for the Log Ratio of Beta Distributions in a Bayesian Update?
Consider a prior distribution $\text{Beta}(\alpha, \beta)$ and $N$ observed Bernoulli($p$) coin tosses with $k$ heads. The quantity I'm interested in is:
\begin{align}
\log \left(\frac{\text{Beta}(p; \...
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Why are beta coefficients in the two linear regressions same? [duplicate]
I tried two linear regressions with the same dependent variable $y$. Let us assume that the dependent and independent variables are centered around 0 to avoid the need of intercept.
The first with 2 ...
1
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Fisher exact test in correlated dataset
Suppose I have n subjects. I have measured them twice with some binary outcomes. Now I want to test whether outcomes measured earlier agree with outcome measured later. Usually, I would need to do ...
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