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0
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2answers
18 views

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 ...
0
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0answers
15 views

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), ...
1
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0answers
23 views

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 $D$ ...
1
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0answers
17 views

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 ...
0
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0answers
23 views

ANOVA analysis in regression

I have an issue regarding ANOVA analysis. Let me explain what I am looking for…You have 3 factors (A,B,C). Now in CCD or BBD you get ANOVA for ...
0
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2answers
55 views

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 ...
0
votes
0answers
14 views

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 ...
1
vote
1answer
19 views

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 ...
1
vote
1answer
28 views

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 ...
0
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0answers
34 views

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 ...
1
vote
0answers
32 views

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 ...
3
votes
0answers
22 views

Covariance of two distinct quadratic forms

Let's say that I have two random vectors, that should belong to the same distribution family, but are distinct. I.e. $\mathbf{Y_{1}} = (Y_{11}, ..., Y_{n1})^{T} \sim D(\mu_1, \Sigma_1)$ and $\...
1
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0answers
29 views

How to test whether social network properties predict a binary outcome?

I'm looking to see if whether social network properties (such as different measures of centrality) predict a binary choice. The first part of the question is, what is the best method to do this? I ...
3
votes
0answers
21 views

Computations of Durbin-Watson quantiles

For some educational reasons I am currently trying to re-compute Durbin and Watsons (1951, Paper II) critical values of the lower and upper bounds of their Test-Statistic (dL and dH), and also table ...
1
vote
1answer
26 views

lower order term has positive prediction in simple regression but negative prediction in quadratic regression

I am using SPSS to conduct a quadratic regression. The IV is positively and significantly related to the DV in a simple linear model. However, after the squared IV is put in the model, the lower order ...
4
votes
1answer
85 views

Distribution of a quadratic form, non-central chi-squared distribution

Definition. Suppose $\mathbf{y} \sim \mathcal{N}(\boldsymbol{\mu}, I_{n \times n})$. Then $$w = \mathbf{y}^{T}\mathbf{y} = \|\mathbf{y}\|^2 \sim \chi^{2}_{n}\left(\theta = \|\boldsymbol{\mu}\|^2/...
2
votes
1answer
50 views

Gaussian distribution sample norm versus mean norm

Consider a Gaussian distribution with mean $\boldsymbol\mu$ and covariance matrix $\mathbf{Q}$, and suppose I take a sample from this distribution and compare its norm with the mean norm. My goal is ...
0
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0answers
20 views

How to estimate a Simple Quadratic Equation

Hello i am quite new to economic application and have a really simple question about estimating a quadratic equation. I have a time series data set with 55 points and want to estimate a quadratic ...
0
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0answers
7 views

Independence of quadratic forms of random variables [duplicate]

If $X$ and $Y$ are two vectors of random variables, such that $X$ and $Y$ are independent, is it true that $X^TX$ and $Y^TY$ are independent? If yes, how do we prove it?
0
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0answers
23 views

covariance of a normal distribution and a quadratic form [duplicate]

I'm working on this problem and am a little lost, can anyone lend their assistance? $$X\sim N_k(\mu, \Sigma)$$ show $$cov(x, x'Ax)=2\Sigma A\mu$$ I tried $cov(x,x'Ax)=cov(x,\sum_{i=1}^k\sum_{j=1}^...
2
votes
1answer
34 views

First two moments of a quadratic form in which the vector and matrix are random (though independent)

$\DeclareMathOperator\tr{\mathrm{tr}}$Let $x$ be a standard normal $p$-variate random variable, which is independent of a symmetric positive definite random matrix $Y$. I would like to compute the ...
1
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0answers
62 views

Quadratic equation system solving analytically or numerically

I have such a nonlinear equation system $x_i=\frac{\sum_{j\neq i}a_{ij}\times\sum_{k\neq i}x_k}{\sum_{k\neq i}x_k-\sum_{j\neq i}a_{ij}}$ where $a_{ij}$s are known coefficients in $[0,1]$. And $x_i$s ...
0
votes
0answers
67 views

Mean of a truncated quadratic function of a normal variable

Suppose you want to compute the mean of the following random variable: $$ V=\left(\frac{z-y}{z}\right)I\left(y<z\right)-\left(\frac{z-b_0}{z}\right)I\left(b_0<z\right) $$ where: $$ y=b_0+b_1x+...
3
votes
1answer
131 views

Expectation of Euclidean Norm and Quadratic Forms

If $\boldsymbol{\beta} \sim \mathcal{N}_p(\boldsymbol{\mu}, \boldsymbol{\Sigma})$, can someone please help me understand why $\mathbb{E}[||\boldsymbol{\beta}||_2^2] = ||\boldsymbol{\mu}||_2^2 + \text{...
3
votes
0answers
98 views

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 ...
0
votes
1answer
15 views

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? ...
5
votes
1answer
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)?...
3
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0answers
68 views

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 $n,p(n)\to\infty$ ...
1
vote
1answer
57 views

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 $X=\left(\begin{array}{ccc}X_1\\X_2\end{array} \right)$...
1
vote
0answers
98 views

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 ...
0
votes
1answer
44 views

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 ...
6
votes
2answers
140 views

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 ...
1
vote
0answers
65 views

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 ...
1
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0answers
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 ...
0
votes
1answer
116 views

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?...
0
votes
1answer
72 views

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 ...
5
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1answer
471 views

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 ...
0
votes
0answers
134 views

Quadratic categorical variable

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 ...
2
votes
0answers
51 views

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 ...
1
vote
1answer
2k views

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 ...
1
vote
1answer
101 views

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 ...
0
votes
0answers
178 views

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. ...
1
vote
0answers
97 views

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). ...
2
votes
1answer
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 ...
3
votes
1answer
91 views

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 ...
0
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0answers
49 views

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 ...
2
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2answers
51 views

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 ...
1
vote
1answer
151 views

Determinant of the covariance matrix in a normal distribution

Suppose a $p \times 1$ vector $x \sim N_p(\boldsymbol 0, \boldsymbol \Sigma_1)$. Now, There is another covariance matrix $\boldsymbol \Sigma_2$. We know that $|\boldsymbol \Sigma_2| < |\boldsymbol \...
7
votes
2answers
1k views

Quadratic Programming and Lasso

I'm trying to perform a lasso regression, which has following form: Minimize $w$ in $(Y - Xw)'(Y - Xw) + \lambda \;|w|_1$ Given a $\lambda$, I was advised to find the optimal $w$ with the help of ...
1
vote
1answer
71 views

How should I interpret a factor that is significant both (1) in linear form in interaction with another factor and (2) in its quadratic form?

Our study aims to identify and understand how several ecological factors relate to parasite abundance in a colonial animal. However, we are uncertain on how to interpret a factor (density) that is ...