Questions tagged [statistics]
Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.
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Isn't the choice of 1 as a threshold for sum-of-squared-errors somewhat arbitrary and poorly motivated?
Suppose we have a set of bivariate data $\{X_i,Y_i\}_{i=1}^n$, and we are trying to use it to construct a linear regression model. Often times, our goal is to minimize the SSE:
$$SSE=\sum_{i=1}^n(Y_i-\...
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Relation between two different forms of autocorrelation
I am trying to understand the Wiener-Khinchin theorem which states that the inverse Fourier Transform of the power spectrum of a continuous function $|E_\nu|^2$ gives the autocorrelation of $E(t)$. A ...
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How to mathematically measure similarity between different families? [closed]
Here is some R code which randomly simulates a family:
...
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The difference between mean and mathematical expectation?
There is common interview question to people pursuing Statistics Career in Africa, especially Kenya and Malawi, is what is the difference between mean. Mathematically, $$\mathbb{E}_{f}(g(X))=\begin{...
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$p$-value and sample size for $\chi^2$ test (or statistical tests in general)
I am about to do a statistical test and while I have some knowledge in mathematics in general, I only have basic knowledge (at best) in statistics. What I want to do is test whether a certain ...
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Is testing for host's knowledge in the Monty Hall Game possible? [closed]
One of the most discussed questions concerning the Monty Hall Game is whether it matters if the host has knowledge. One question that is not discussed that frequently is if we can actually test the ...
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Is the posterior probability of a credible set evaluated after observing the sample?
For my bayesian statistics class I'm given this definition of credibile set:
Let $\alpha \in(0,1)$. A $(1-\alpha)$-credible set associated to the
posterior distribution $\Pi(\,\cdot\, \mid X)$ is any ...
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Statistical motivation for the Fisher-Rao metric tensor
I have a really basic question about information geometry that I still can’t quite grasp...
I’ve looked through various posts in this forum and, of course, reference works in the field, but this ...
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How do you actually set up the linear system in moving least squares?
The MLS setup depends on the minimizaiton of:
$$ E(p) = \sum_{i \in I} (p(x_i) - f(x_i))^2 \theta(\|x - x_i\|)$$
Let's assume $\theta(x) = e^{-hx^2}$ for now.
If I understand correctly $p$ is a ...
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Does the theory of symmetric functions show up in statistics?
Given an I.I.D sample $X_1,...,X_n$ and parameter $\theta$, a point estimator $\hat{\theta}$ of $\theta$ is a function of the sample:
$$\hat{\theta}=g(X_1,...,X_n)$$
It follows from independence that ...
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Getting contradictory statistics formula from linear algebra
for some context I've recently been revisiting statistics and have been deriving the formulas in linear algebra terms, since in my opinion they are more compact and easier to remember. However this ...
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LRT for Poisson multinomial
I am having trouble defining a likelihood ratio test (LRT) statistic for a Poisson multinomial distribution (sum of several independent but non-identical categorical distributions), in the context of ...
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Compute z-score
Knowing that $\sum_{i=1}^{10} x_i = 850$ and that $\sum_{i=1}^{10} x_i^2 = 76610$, I want to know what is the confidence we can attribute to $\mu \in (70.4, 90.6)$, when $X$ is a random normal ...
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Determine odds based on given quantities
I'm trying to determine the odds of pulling certain cards from sports card packs. I think my Math is steady until it comes time to figuring out what it takes to pull a specific card.
The product is ...
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Removing the gamma function in $\frac{(n\beta)^{2n}}{\Gamma(2n)} \int_{0}^{\infty} s^{(2n-1)-1} e^{-n\beta s} \, ds$
Background
In my old lecture notes, I stumbled upon this problem, where the text in red confused me:
We have seen that, if we have a random sample $X_1, \dots, X_n \overset{\text{i.i.d.}}{\sim} \text{...
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