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40 views

Stationarity and Regression

apologies this might turn out to be a bit on the simple side, but I've been thinking this through and haven't quite found the right approach. Suppose I have a bunch of time series (say ...
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0answers
32 views

Functional approximation that vanishes at infinity

I have a function $f(x)$ that I wish to approximate using a linear combination of basis functions $$ \hat{f}(x) = \sum_{i=1}^k c_i \varphi_i(x). $$ The approximation is done via an orthogonal ...
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0answers
43 views

Derivation of gradient of SSE in Geodesic Regression

On page 79 (or page 5) of this this paper the gradient of the SSE of the Geodesic model is described explicitly. My question is how are these equitations derived in detail; where can I find the ...
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0answers
20 views

Encoding and Transforming Data for a Logistic Regression

When running a logistic regression, the result of the regression is a value that could fall in $(-\infty, \infty)$. You run it through the logistic function and get a value in $(0, 1)$. So far, so ...
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3answers
300 views

When does a Vandermonde-like matrix have full rank

I have a matrix which is similar to Vandermonde matrix except that the entries are monomials of degree $d$ polynomial in 2 variables. Each row has the following form: $X_{i}= [1, x_{i}, y_{i}, ...
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0answers
114 views

Is there an efficient way to compute the “complete subset regression”?

Background: Let $X \in \mathbb{R}^{N\times K}$ and $y \in \mathbb{R}^{N\times 1}$ be data for a regression problem. The aim is to find $\beta \in \mathbb{R}^{K\times 1}$ such that $X\beta \approx y$ ...
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1answer
104 views

Checking the intersection of two sets

Let $E\subset{\mathbb R}^n$ be a set of the type $I_1\times \dots \times I_n$, where $I_k$ are real intervals, and $X$ be and $n\times p$ real matrix. Suppose also that $rank(X)=p$ and $n>p$. Is ...
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1answer
70 views

Fitting a quadratic using regression when the y-intercept needs to be 0 [closed]

I'm trying to fit a quadratic $a_0 + a_1x + a_2x^2$ by Polynomial Regression: $$ \begin{pmatrix} n & \Sigma x_i & \Sigma x_i\\ \Sigma x_i & \Sigma x_i^2 & \Sigma x_i^3\\ \Sigma ...
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0answers
59 views

How to find all least-square solutions [closed]

I was looking at numpy's lstsq to find a least squares solution of an equation system when the following occurred to me: Given the points (0,0), (3,4), (4,3), if I ...
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0answers
20 views

Regression with correlation structure

I have a theoretical question about regression models. Let's say I measured multiple responses from $n$ subjects and these responses are correlated with each other. For example, let's say I measured ...
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1answer
423 views

Minimizing sum of absolute deviations

Suppose we want to find coefficients $b$ in $\underset{b}{\operatorname{argmin}} \displaystyle\sum\limits_{i=1}^n | y_{i}-b_{1}x_{i}-b_{0}\mid$. If we rewrite this problem in terms of linear ...
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231 views

Testing contrasts in statistics: Is this provably a hard problem, or not?

Scheffé's method for identifying statistically significant contrasts is widely known. A contrast among the means $\mu_i$, $i=1,\ldots,r$ of $r$ populations is a linear combination $\sum_{i=1}^r c_i ...