Questions tagged [mathematical-statistics]
Mathematical theory of statistics, concerned with formal definitions and general results.
7,827
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Pearson chi square and correlation
My data are ordinal
Pearson chi squared test value is 4.664
And asymp sig is 0.97 so the data are independent
However pearson's R =-0.309
And the approx sig=0.037
Can they be independent and ...
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How to find the marginal distribution of $p_k$ in multinominal regression
Given a multinominal regression the probability of a certain class $k$ is a function of predictors. How would we find analytically the marginal probability of $p_k$ given we know the distribution of ${...
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Recreate `lm` Categorical Regression
Consider the code, which contains regression using lm of two categorical and one continuous variables without interaction using data from the correct model:
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Is considering a specific distribution necessary before computing an average?
Many times, I compute averages of variables without considering distributions at all, and I use those computed averages to represent measures of variables in my data without mentioning specific ...
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Why the contribution of a categorical value in SHAP trained on Catboost differs from observation to observation
Context
Let's imagine I am interested in predicting sepal length in the iris dataset using catboost.
Objective
My main objective is understanding the effect of each categorical value for ...
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Perfusion Analysis Counts as Survival Analysis?
In perfusion analysis, the patient is injected with some dose of medicine. A machine detects, over time, the dose of medicine in the patient's body. In other words, the data for each patient is time ...
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Combine back- and forecast errors for cross-validation
Suppose I have a procedure to predict the timeseries value $Y_{t+k}$, where $t$ is the current period and $k \geq 1, 2, \dots$. Now, I want to estimate the procedure's out-of-sample performance. The ...
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Consistency of a test - convergence of quantile
I have given statistical model $((0,1)^n, \mathcal{B}(0,1)^n,\mathcal{P}_n)$, where $\mathcal{P}_n=\{ P_{\theta}^{\otimes n} \ |\ \theta \in (0, \infty) \}$ and each $P_{\theta}$ has density function $...
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Nonhomogenous Geometric Distribution Approach
I am trying to solve this problem by considering a geometric distribution with unequal probabilities.
First, I am using the Irwin-Hall Distribution to deduce that for n independent uniform random ...
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How to estimate the CI of RERI [closed]
This thread is involved in statistical tech to measure interactions. The RERI is short for "relative excess risk due to interaction". I know it's quite a bit difficult to understand but, to ...
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+50
How to disentangle effects of components in system?
I have a system where one property (delay) depends on its components, a valve $V$ and the piping $P$ in a hydraulic system:
$d = f(V, P)$
I have reference measurements with one type of valve and ...
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Power of One Sided t-test
Let $X_1, \ldots, X_n$ be a sample from $N(\mu, \sigma^2)$ for unknown $\mu \in \mathbb{R}$ and unknown $\sigma > 0$. Fix $\mu_0 \in \mathbb{R}$. The one-sided hypothesis is $H_0: \mu \leqslant \...
- 456
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Proof of Strong consistency of Beta posterior distribution
Suppose that we have random variable $X_{1}, X_{2}, ..., X_{n} \sim^{iid} \text{Bernoulli}(p_{0})$ with $p_{0}$ true unknown probability in $[0,1]$. Now, I want to implement Bayesian machinery to ...
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An example problem of converting a maximum likelihood problem into a restricted maximum likelihood problem
I have a question about this derivation. What is an example value of the actual matrix $A'$ such that $A'X=0$, $A'A=I$, and $\frac{1}{n}\Sigma((A'Y_{i}-mean(A'Y))^{2}=\frac{1}{(n-1)}\Sigma((Y_{i}-...
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Why do we assume samples have the same variance when deriving standard error? [closed]
In all derivations I've seen of the standard error formula $\sigma/\sqrt{n}$, it is assumed all the samples in the sampling distribution have the same variance ($\sigma^2$). Why is it assumed they all ...
