# Tagged Questions

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### Effect of quadratic term when variable's range is negative

I am running a Linear Model where I want to include a quadratic term. The dependent and the explanatory variables are all in logarithmic terms. Further, due to Log transformation the range of X is ...
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### Quadratic programming in SVM is inefficient in higher dimension?

I am learning SVM from this lecture - https://www.youtube.com/watch?v=eHsErlPJWUU - though I have some questions. Let's say we have d features: x1, x2, x3..., xd. And we have p sample: x1(1), x2(1), ...
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### effect of linear term on quadratic programming

What's the impact of linear term ($d$) on quadratic programming problem ($P$) described as follows \begin{align*} \min_x d^T x + 1/2 x^T D x\\ \text{such that }A^T x \geq x_0 \end{align*} where $D$ ...
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### Compute a Quadratic discriminant analysis (QDA) in R assuming not normal data and missing information

In this course, the professor is saying that we can compute a QDA with missing data points and non-normal data (even if this assumption can be violated). But the problem is that I don't know any ...
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### ANOVA analysis in regression

I have an issue regarding ANOVA analysis. Let me explain what I am looking forâ€¦You have 3 factors (A,B,C). Now in CCD or BBD you get ANOVA for ...
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### How to interpret Quadratic Terms

I'm answering a practice exam questions, and having trouble with one on quadratic terms. Could someone give me a quick summery of 1) why they are sometimes included? 2) How to interpret them? In ...
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### Is there a minimum to number of quadrats?

When creating quadrats, is there a minimum to the amount of quadrat samples I split my area to? For instance, can it be 2 by 2 (only four squares?) Can it be a single quadrat (no idea why would I need ...
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### Do quadrats have to be equal in size?

I'm doing a quadrat analysis of point pattern. My study area is 2.3m by 2.3m. Can I have quadrats of 1sqm or does it have to be equal area? If quadrats are 1sqm, then four of them would be of full ...
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### Quadratic term and categorical predictors

I have a quick question about the use of quadratic term in GLMM. Can I use it with categorical variables? I read somewhere that its use is restricted to continuous predictors and the thing is that I ...
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### Cox PH model with quadratic effect interpretation

I'm fitting a Cox model with non-linear continuous variable with and without a time varying effect (to correct non-PH). My goal is to get risk ratio (hazard ratio) associated with X. I have the Cox PH ...
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### Testing for Unit Roots with Quadratic Trends in Stata

I understand that Dickey-Fuller test could test for a unit root with drift and deterministic time trend. $$\nabla y_t = a_0+a_1t+\delta y_{t-1}+u_t \$$ What are the tests for unit root with ...
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### Modeling quadratic function parameters as a function of variables

I'm modeling a response variable that varies seasonally. The pattern is relatively well described by a quadratic function. As the data have been collected over many (~50) years, I'm interested to ...
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### Variance estimator of quadratic term of Cox PH model

I have a failure time data set. I want to fit Cox PH model with quadratic term like $h(t;x)=h_0(t)*exp(x\beta_0+x^2\beta_1)$ What will be the mathematical formula for variance of quadratic term? ...
371 views

### Relationship between Gram and covariance matrices

For a $n\times p$ matrix $X$, where $p \gg n$, what is the relationship between $X^{T}X$ (scatter matrix, on which covariance matrix is based) and $XX^{T}$ (outer product sometimes called Gram matrix)?...
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### Does a “pruned” i.i.d. multivariate sample behave as the i.i.d. sample?

Let $z_1,\cdots,z_n$ be $n$ points drawn i.i.d. from $\mathbb{C}N_p(0,\Sigma_n)$. The distribution of the covariance $S_n=\frac1n\sum_{i=1}^n z_i z_i^*$ is well known in the limit as $n,p(n)\to\infty$ ...
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### Prove that the distribution of $Q$ is chi-squared with $p_2$ degrees of freedom

Suppose $X$ is a $p$-dimensional vector following $N_p(\mu,\Sigma)$ distribution, where $\mu$ is $p$-dimensional and $\Sigma$ is $p\times p$. Let $X=\left(\begin{array}{ccc}X_1\\X_2\end{array} \right)$...
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### Interpreting scaled betas for quadratic terms in a negative binomial regression

I created a negative binomial model where the final model included 5 quadratic predictors (each with a corresponding linear term). I am considering two ways to interpret the beta coefficients for each ...
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### estimators with singular covariance matrix

Suppose I have 2 vectors of random variables $\boldsymbol\theta_1 \in \mathbb{R^n}$ and $\boldsymbol\theta_2 \in \mathbb{R^m}$ with asymptotic covariance $\Sigma_1$ and $\Sigma_2$ respectively. I want ...
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### A strange step on a proof about the distribution of quadratic forms

The following theorem comes from the 7th edition of "Introduction to Mathematical Statistics" by Hogg, Craig and Mckean and it concerns the necessary and sufficient condition for the independence of ...
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### Method to minimize a quadratic form

How should I minimize a quadratic form $g(x)^TA(x)^{-1}g(x)$ with respect to $x$, where $g$ is a vector which depends on the vector $x$? This quadratic form is obtained from a quasi likelihood ...
237 views

### Correlation between two quadratic forms of Gaussian random vectors

I want to approximately calculate the correlation between two quadratic forms of two Gaussian random vecotrs (of course these are in fact non-Gaussian densities). Does anyone know the derivation of ...
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### For a quadratic form to minimize with a L2 regularization term, is the gradient of the solution collinear to the solution?

Say you minimize a quadratic form f with a L2 regularization term (g = f + L2_term). The solution of minimizing g is x*. Is the gradient of f applied to x* collinear to x* as the figure below suggests?...
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### Expectation of a fractional form of chi squared

I have been trying to calculate or find a result for the expectation $$\mathbb{E} \left[ \frac{w^\top D^2 w}{1 + w^\top D w} \right]$$ where $$w \sim \mathcal{N}(0,I_N),$$ and $D$ is a diagonal ...
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### Parallel regression assumption

In ordinal logit models, do I violate the parallel regression assumption if I include a quadratic term for a nonlinear relationship? Because then it would mean that the coefficients are not in the ...
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My model includes a categorical independent variable. The graphical analysis suggests that the relation between this variable and the dependent one could be quadratic. As regards including a squared ...
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### Proving the given quadratic form is chi-squared $k$

Suppose $\underline{X}$ is an $m$-dimensional vector following multivariate Normal distribution i.e. $\underline{X}$~$N_m(\underline{\mu},\Sigma)$ where $\Sigma$ is positive definite. Let $B$ be a ...
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### Plotting a polynomial regression with its confidence interval of 95% in R

I have been trying for a while plotting a polynomial regression using R. I have read several libraries, as ggplot2, qplot, etc, with no succeed. The next are my data: I normally use the R GUI called ...
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### How to fit a single quadratic term to a regression

I have a high dimensional multivariate model and am fitting linear weights to each of the $N$ free variables using a classic stable SVD matrix solver. This works. I want to improve the fit by using a ...
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### Single group with repeated measures using R? - Trend analysis (linear, quadratic effect)

I wonder how to get the repeated measures analysis of variance using R. My data is like this. ...
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### quadratic endogenous variables in R

As part of ongoing research I'm to test a certain model on some data. One of the questions asked (c.f. one of the hypotheses) involves estimating the quadratic term of an independent variable (in R). ...
178 views

### Linear regression with an inequality constraint

I am looking for an efficient way of finding a linear fit $Mx = y$ subject to an inequality constraint: $\frac{|x_2|}{\sqrt{x_3^2 + x_4^2}} \geq a$, with $a \geq 1$. The rectangular matrix $M$ is ...
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### Weird pdf of a quadratic function of a N(0,1) variable: miscoding or big rounding error?

I would like to calculate the pdf of a random variable y defined by : y=c+b*x+a*x^2 The pdf is a non-central chi-squared distribution. For a>0, it should be equal ...
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### Can I determine whether two quadratic slopes differ significantly?

I know that there are ways to compare two linear functions to determine whether the slopes of the functions are significantly different. However, I'm wondering whether there is any way to compare ...
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### Testing equality of two X values in quadratic regression

So let's say we have a quadratic relationship between two variables, y and x. Graphically, it is U-shaped. However, there is also a linear component to it, such that the left curve is lower than the ...