# Questions tagged [quadratic-form]

A quadratic form is a homogeneous polynomial of order two.

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### what is the difference between MDA and LDA?and differences between LDA and QDA? I need compelet answer thanks for your help

what is the difference between MDA and LDA?and differences between LDA and QDA? I need compelet answer thanks for your help
0answers
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### Clarification regarding $(X'BX)(X'AX)$ distribution

Assume $X = (X_1, \ldots, X_n)' \sim \mathcal{N}(0, \Sigma)$ is a random normal vector. I'm looking for the distribution of the following form: $$Z = (X'BX)(X'AX)$$ here $X \in \mathbb{R}^{n \times 1}$...
1answer
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### Manipulation of quadratic form

How is this derivation obtained? It seems like it is possible to do so from first principles for using the series definition for quadratic form, but that seems tedious. Is there a faster way to ...
0answers
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### Multivariate normal distribution -testing a quadratic form of mean vector

Suppose $X_{1},X_2,...,X_n$ are i.i.d.observations from a multivariate normal distribution $N(\mu,\Sigma)$ where $\Sigma$ is known. Assume that $a$ and $b$ are given vectors. Use the likelihood ratio ...
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### Transformation of dependent normally distributed random variables

If $Y_1,Y_2,...Y_n$ are normally distributed random variables with mean $E(Y_i)=\mu\;,Var(Y_i)=\sigma^2\;and\;Cov(Y_i,Y_j)=s[i,j=1,2,...,n;i\neq j]$ and we take the transformation $Z_i=Y_i^2$, then ...
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### Distribution of quadratic form?

Let $\mathbf{y = X \boldsymbol{\beta} + \epsilon}$, where $\mathbf{X} \in \mathcal{R}^{N\times p}$, $\boldsymbol\beta \in \mathcal{R}^p$ and $\boldsymbol{\epsilon} \sim N(0,\sigma^2 \mathbf{I}_N)$. ...
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### quadratic regression - model assumptions not respected

I've just finished performing a quadratic regression. The results are significant, but when plotting the residuals, I noticed that the assumptions of the model (i.e. homogeneous variances and normal ...
0answers
37 views

### Convert back standardized parameters for a quadratic fit

I have a model with standardized data: $x' = \frac{x - \bar{x}}{S_x}$ $y' = \frac{y - \bar{y}}{S_y}$ I’m trying to figure out how to convert back the coefficients of a quadratic fit to the original ...
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### Panel data OLS regression: plot and quadratic fitting line

I am conducting an OLS regression panel data analysis with package PLM in R. I use the following script to obtain a plot and fitting line of variables D and ...
2answers
177 views

### Assessing model fit of two models by computing t-test on coefficients in R

I am attempting to assess whether my explanatory variable of "startingpos" is best modelled via a quadratic regression model or a linear regression model. One way I can do this is to compute the ...
1answer
449 views

### Fitting a quadratic regression in R

I am trying to fit a quadratic regression model in R. Here is an example of my dataframe: ...
1answer
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### Including a quadratic effect for an ordinal variable in a regression analysis

It's common for many datasets to have ordinal versions of numerical variables, such as age groups (e.g. "Under 20", "20-30", "30-40", etc.) or time groups (e.g. "Less than 15 minutes", "15-30 minutes",...
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### Variance Ratio Formula

I've been trying to minimize/maximize the ratio of quadratic forms given by $$Q(c)=\frac{c^\top \Sigma c}{c^\top \text{diag}(\Sigma) c}$$ where $\Sigma$ denotes a covariance matrix of some $n$-...
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### Variance of Quadratic form

From the Wikipedia In general, the variance of a quadratic form depends greatly on the distribution of $\varepsilon$ . However, if $\varepsilon$ does follow a ...
1answer
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### Expectation of Quadratic Form with Two Random Vectors

Assume I have two independent $(N \times 1)$ random vectors, $\epsilon_{1} \sim N(0,\Sigma_1)$ and $\epsilon_{2} \sim N(0,\Sigma_2)$. We could assume $\Sigma_1=\Sigma_2$ for my purposes but a general ...
0answers
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### Self-Study: If $x \sim \mbox N_p(\mu; V)$ and A is a matrix then how to show that $E[(x-\mu)(x-\mu)'A(x-\mu) = 0$?

If we assume the random vector $x$ to be normally distributed with $N_p(\mu; V)$ then $E[(x-\mu)(x-\mu)'(x-\mu)] = 0_p$. If I am not mistaken, this can be shown using the moment generating function of ...
1answer
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### Determine statistical difference of slopes of quadratic relationship in a Poisson regression

I'm looking for a statistical or mathematical way to test the difference between two slopes. Others have asked related questions but my problem is quite particular. I'm running a Poisson regression ...
1answer
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### Maximization of quotient of quadratic forms in linear regression

I would like to find maximum of the following function: $$I = \max_{a\in \mathbb{R}^p} \frac{(a'\hat{\beta})^2}{S^2a'(X'X)^{-1}a},$$ where $X$ is a design matrix and of course $Y$ is normally ...
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### Covariance of Two Quadratic Forms

We're looking for the $\operatorname{Cov}\left[x^T A x, ~x^T B x\right]$ where $x$ is random variable and mean-centered, but not independent and $A$ and $B$ are symmetric matrices. The fundamental ...