# Tagged Questions

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### Standardizing response variable in shrinkage/regularization

I know that I should standardize my predictors before estimating something like Lasso. But what about the response variable? Do I standardise this as well? Only ...
18 views

### Lasso-ing the order of a lag?

Suppose I have longitudinal data of the form $\mathbf Y = (Y_1, \ldots, Y_J) \sim \mathcal N(\mu, \Sigma)$ (I have multiple observations, this is just the form of a single one). I'm interested in ...
73 views

### When would I choose Lasso over Elastic Net

What are the scenarios where Lasso is likely to perform better than Elastic Net (out of sample prediction)?
28 views

### Whitening a dataset with fewer observations than variables

I have a k x n dataset where k equals the number of variables and n equals the number of observations per variable. I know these data are correlated and I would like to whiten them with the ordinary ...
353 views

### How to get confidence interval on population r-square change

For sake of a simple example assume that there are two linear regression models Model 1 has three predictors, x1a, x2b, and ...
64 views

### Selecting a Bayes shrinkage prior

I'm looking for a way to integrate prior knowledge about a parameter in a context equivalent to Bayesian hierarchical models. I come from frequentist background and I'm uninitiated in hierarchical ...
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### Initializing Variables using Shrinkage

I have a user-user model which which users can rate their friendships(r) with others and also can have activities with them(a). I am using Matrix Factorization and Gradient Descent for updating the ...
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### Is there a theoretical basis for the shrinkage used in Boosted Regression Trees?

In Gradient Boosted Regression Trees, a shrinkage $\nu$ is often applied as: $$f_t(x) \leftarrow f_{t-1}(x) + \nu h(x)$$ where $h$ is the regression tree learned by fitting the tree to the gradient. ...
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### What is the adjusted R-squared formula in lm in R and how should it be interpreted?

What is the exact formula used in R lm() for the Adjusted R-squared? How can I interpret it? Adjusted r-squared formulas There seem to exist several formula's to calculate Adjusted R-squared. ...
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### adjust rating based on number of experiences

Suppose I am using a restaurant rating as an explanatory variable in a regression. The rating is defined as $R=\frac{G}{G+B+N+S}$, where $G$ is good, $B$ is bad, $N$ is neutral and $S$ is silent. I ...
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### Estimation After Selection on Non-central F Random Variables

Suppose that you observe $F_1,F_2,\ldots,F_k$ each independently. drawn from non-central F distributions with common, known, d.f. $\nu_1, \nu_2$, and with (unknown) non-centrality parameters ...
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### How can I use “partial pooling” to shrink cells with a small sample size towards the mean in a contingency table?

How can I use "partial pooling" to shrink cells with a small sample size towards the mean in a contingency table? I am interested in the proportions within each cell with a positive response. To ...
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### Are there any extensions to the James-Stein estimator for cases of dependent variables?

Are there any extensions of the James-Stein estimator for case of dependent variables? I've done numeric experiments with the James-Stein estimator on correlated normal variables (5-10 variables, ...
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### Proportion Estimates - Shrink to the Mean Based on Sample Size

Set-up: One of the fundamental elements of direct marketing is choosing which lists of prospects to select and send an offer to. There are hundreds of lists on the market to choose from and each list ...
1k views

### What problem do shrinkage methods solve?

The holiday season has given me the opportunity to curl up next to the fire with The Elements of Statistical Learning. Coming from a (frequentist) econometrics perspective, I'm having trouble grasping ...
6k views

### What is the lasso in regression analysis?

I'm looking for a non-technical definition of the lasso and what it is used for.
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### Using monomvn to impute monotone missings

I am attempting to use the monomvn package to impute monotone missings. I've followed the basic example: data(cement.miss) out <- monomvn(cement.miss) ...
523 views

### Optimal penalty selection for lasso

Are there any analytical results or experimental papers regarding the optimal choice of the coefficient of the $\ell_1$ penalty term. By optimal, I mean a parameter that maximizes the probability of ...
185 views

### Distribution of 'unmixed' parts based on order of the mix

Suppose I have paired observations drawn i.i.d. as $X_i \sim \mathcal{N}\left(0,\sigma_x^2\right), Y_i \sim \mathcal{N}\left(0,\sigma_y^2\right),$ for $i=1,2,\ldots,n$. Let $Z_i = X_i + Y_i,$ and ...