# Questions tagged [linear]

For statistical topics which involve the assumption of linearity, for example, linear regression or linear mixed models, or for the discussion of linear algebra as applied to statistics.

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108 views

### Is multivariate Cauchy stable?

I am trying to prove (if possible), for given $A_{n\times n}$ and $B_{n\times n}$, there exists a $C_{n\times n}$ satisfying $$A\pmb{X}_1 + B\pmb{X}_2 \stackrel{D}{=} C\pmb{X},$$ where $X_1, ~X_2$, ...
595 views

### Which theorem in Cover's 1965 paper is actually referred to as Cover's Theorem?

Cover's Theorem is stated on Wikipedia (and similarly elsewhere) as A complex pattern-classification problem, cast in a high-dimensional space nonlinearly, is more likely to be linearly separable ...
893 views

### How to test a linear relationship between log odds and predictors before performing logistic regression?

In case of a linear regression, it's easy to test a linear relationship between a continuous dependent variable and each independent variable. For example, I can plot a scatter plot between the ...
3k views

### Is the Naive Bayes family of classifiers linear?

There are a lot of places where you'll see the proof that Naive Bayes classifiers are linear, like this and this. But they always assume a special case of the family of Naive Bayes classifiers which ...
487 views

### Is lasso always outperformed by adaptive lasso?

I have been reading some papers and I understood that adaptive lasso has the Oracle properties which lasso lacks. Does that mean adaptive lasso always better than lasso (let's focus on the simple ...
102 views

### Method to forecast correlate univariate time-series (with trend, seasonality) via regression

I have two univariate time-series with seasonality and trend--dt1 and dt2. I believe that dt1 and dt2 are strongly correlated, both through a few statistical test (see below) and that in my field dt2 ...
283 views

### Do results from the lme-function require adjustment of p-values?

If I run a linear mixed model with the lme() function and get results like these (comparing the score of 4 treatment groups against a placebo group): ...
362 views

### Analytical linear regression vs cost function

I'm trying to fit data to a line $y=ax+b$ (you can download it in this gist). You can see a fit in the next image: To do so, I'm using analytical methods of minimization of the cost function, defined ...
135 views

### Linear and Nonlinear Components of a Time Series

I am starting to develop a hybrid ARIMA-ANN model for forecasting. Most of the journals I read mention mostly a linear component for ARIMA and a nonlinear for ANN. How can you know which components ...
94 views

### Decomposing a locally stationary covariance matrix

Say I have a non-stationary Gaussian Process with a square exponential covariance whose shape varies throughout space. The covariance entries are: $$K_{ij} = N(|x_i-x_j|,\sigma_i^2+\sigma_j^2)$$ ...
140 views

### Adjust linear regression penalty for under/over-estimations

Basically I have a case where under-predictions are worse than over-predictions. Is there a way to penalize the linear regression model during training according to some predefined ratio? E.g. I want ...
44 views

### What is the significance of “orthogonal” vectors in statistics?

So I am reading What does orthogonal mean in the context of statistics?, and there are contradictory answers. The most upvoted answer says that "Therefore, orthogonality does not imply ...
38 views

### log transform in linear regression

Assume we have a data set and the theory suggests to model $Y \sim X$. We apply a simple linear regression and get the following: Next, let us make a log transform of both $X$ and $Y$. The result is ...
167 views