A quadratic form is a homogeneous polynomial of order two.

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### Distribution of the correlation coefficient based on quadratic forms

Let $x,y$ be two independent random correlated vectors following the same multivariate (real or complex) centred normal distribution, and let $A$ be a non-negative linear operator. We can read here, ...
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### Specifying interactions, quadratics and ratios in regression model

I would like to model a linear regression with the dependent continuous variable y and the independent continuous variables x and z: The interaction of x and z is expected to increase y, but y is ...
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### Cut-off based on an ordinal variable in unbalanced panel data

I am currently looking for an appropriate statistical analysis for my research questions. I have a continuous variable (score) and an ordinal variable (test). Score is quadratically related to Test, i....
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### Propensity matching affects significance of polynomial degrees differently

I have a regression as follows: $$y = \alpha + \mu L + \beta_1 x + \beta_2 x^2 + \varepsilon$$ where L is a dummy, and x is a control variable. Both $x$ and $x^2$ are significant when I run the ...
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### Formulas, approximations, or bounds for $\mathbb{E}\left( \frac{X}{\lVert X \rVert} \right)$, $X\sim N(\mu, \Sigma)$?

In another question, I asked for $\mathbb{E}\left( \frac{X}{\lVert X \rVert} \right)$, in the case where $X \in \mathbb{R}^d \sim N(\mu, I_{d})$. Somebody posted an exact formula based on the symmetry ...
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### When is an interaction in quadratic regression significant?

I run a regression with a continuous variable $x_2$ and a binary grouping variable $x_1$. We suppose that the effect of $x_2$ is quadratic on the dependent variable $y$ and our question is whether the ...
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### How to interpret interactions involving quadratic terms in a GLM?

I'm trying to interpret the output of a GLM from a tutorial that models species abundances as a function of environmental data and species traits. The function ...
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### Expectation of two Quadratic form

Assume $\mathbf{h} \in C^{N \times 1}$ is a Gaussian vector with zero mean and Covariance matrix $\mathbf{R}$. Also $\mathbf{A} \in C^{N \times N}$ is a deterministic diagonal matrix. In this case, ...
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### How do I calculate the variance of a Hermitian form?

Suppose $\mathbf{x}\sim\mathcal{CN}\left(\mathbf{0},\mathbf{I}_n\right)$ is a circular complex Gaussian random vector, and $\mathbf{Q}$ is a Hermitian matrix. How do I calculate the variance of the ...
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### Interaction between quadratic term and dummy variable

Suppose I have a linear regression: $Y=\beta_1+\beta_2X+\beta_3X^2+\beta_4D$ where $D$ is a dummy variable that takes value 0 and 1. If I want to examine if the effect of $X$ on $Y$ for $D=0$ and $D=1$...
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### State space model equation

I would appreciate your help on the following I have a quadratic equation and need to write it in a state space format according to a model below. My equation is the following below, where T is the ...
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