A message from our CEO about the future of Stack Overflow and Stack Exchange. Read now.

# Questions tagged [theory]

For questions about statistical theory. Always include a more specific tag as well.

233 questions
Filter by
Sorted by
Tagged with
11 views

### Theory: When to use one multi-factorial ANOVA vs. many one-factorial ANOVAs

I was recently peer reviewing a paper that used statistical tests in an odd way that didn't seem right to me. However, I'm not an expert so just wanted to talk theoretically about some of the things I ...
8 views

### Understanding Spectral Density of a time series in terms of Regression on Sinusoids

This may be a very trivial question but I would like to understand spectrum density of a time series in terms of regression. This is what I know from reading on the net: A time series can be ...
26 views

### A good literature for statistical learning theory

any recommendations for good literature on statistical learning theory? I mean, something what goes into more details than Elements of Statistical Learning, in terms of losses, empirical error ...
20 views

### Maximum sample size for one-way ANOVA?

Lists of requirements for one-way ANOVA include the following: Samples should be mutually independent Samples should be from a population with a normal distribution Samples should have the same ...
38 views

### Can the AUC (logistic regression) be used as a measure of quality of the model? [duplicate]

If I have a good measure of the AUC, what does it tell me in relation to the model and its variables?
15 views

### How do you prove that the following 2 hypothesis classes' VC-dimensions are equal?

Given a hypothesis class $H=\{h:X\to\{0,1\}\}$. Let $c\in H$ be the correct predictor. Denote $H^c = \{c\Delta h:h\in H\}$, where $c\Delta h=(h\backslash c)\cup (c\backslash h)$. Please prove that ...
65 views

### Learning from multiple very varied data sets?

Suppose we have a set of objects $X$ (e.g. individual humans). Suppose also that humans can be described by a set of (potentially very high-dimensional) variables $V_i$, (e.g. $V_1$ is a picture of ...
60 views

40 views

### Why isn't the least squares predictor $\Phi(\Phi^\top\Phi)^{-1}\Phi^\top$ simply the identity matrix? [duplicate]

Given target vector $y$. Want to predict it using linear regression $h(w) = w^Tx$ Let $\Phi$ be the least squares matrix, i.e., $\Phi = \begin{bmatrix} x_1^\top \\ \vdots\\ x_n^\top \end{bmatrix}$ ...
39 views

### Operator Theoretic Perspectives on Bayesian Inference

On the Wikipedia page for conjugate prior there is a section "Analogy with Eigenfunctions", which describes a metaphor where observation of data is seen as a "linear operator" on the space of ...
31 views

### multivariate linear regression without b_0 [duplicate]

I created a multivariate regression following the scheme $$y = \beta_0 + \sum^n_{i=1}\beta_i*x_i$$ and got an average deviation ofaround 5%. When I tried the regression without the $\beta_0$ I got a ...
363 views

### ELI5: The Logic Behind Coefficient Estimation in OLS Regression

Like a lot of people, I understand how to run a linear regression, I understand how to interpret its output, and I understand its limitations. My understanding of the mathematical underpinnings of ...
110 views

### Type I and Type II errors in Hypothesis Testing

I am confused about the last highlighted sentence regarding finding a subset S, for which BOTH Type I and Type II error probabilities are 0. For $P_\theta S$, which is the probability with which we ...
163 views

### R: how is the Pr(>|z|) in the results of glm.fit calculated and why?

I've been searching but I can't find anywhere an explanation of how the Pr(>|z|) column is calculated in the results of R's glm.fit function. I would really appreciate: a) an explanation so I can ...
38 views

### 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 ...
Short form: How can I correct two p-values computed from normal distributions to account for the fact that part of the samples overlap? Long form: I have a sequence of i.i.d RVs of length $n$. The ...