kurtosis
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R-squared is equal to 81% means what?
8 votes

An R-squared is the percentage of variance explained by a model. Let's say your data has a variance of 100: that is the sum of squared errors versus the mean and divided by $N-1$ (the degrees of ...

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Examples of Simpson's Paradox being resolved by choosing the aggregate data
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8 votes

I can think of a topical example. If we look at cities overall, we see more coronavirus infections and deaths in denser cities. So clearly, density yields interactions yields infections yields deaths, ...

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In comparison with a standard gaussian random variable, does a distribution with heavy tails have higher kurtosis?
4 votes

Heavy Tails or "Peakedness"? Kurtosis is usually thought of as denoting heavy tails; however, many decades ago, statistics students were taught that higher kurtosis implied more "...

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Which summary statistics are always nonnegative? [just for fun]
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4 votes

Range, IQR, and really any quantile interval lengths; standard deviation/variance, kurtosis (not excess kurtosis), and all other even-power moments; and, likelihood and other chi-squared statistics (e....

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Why isn't simulation showing that ridge regression better than linear model
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4 votes

You are doing nothing wrong. Ridge regression, the LASSO, and other penalized-coefficient regressions yield biased estimations. The idea is that maybe accepting a little bias will greatly reduce the ...

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Nonparametric theory textbook(s)?
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3 votes

I would recommend A Distribution-Free Theory of Nonparametric Regression by Györfi, Kohler, Krzyżak and Walk. It looks like what you are looking for: proofs use sigma fields as needed, there is plenty ...

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Finding anomaly using statistical distributions
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3 votes

One approach would be to use a chi-square test. To do this, you would estimate the overall distribution of sales in various genres from all of the data. For example, say your data revealed this ...

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How regression adjusts categorical variables?
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3 votes

The answer depends on contrasts: how you code these factors and what is your baseline. A lot of software operates from a perspective of experimental analysis and so takes the first factor level as the ...

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LMM: fixed effect significant in complex model, but not in reduced model
3 votes

This looks like you have a problem with multicollinearity: trait1 and trait3 are correlated. You can imagine creating such a scenario like so: Find a covariate (we'll call it trait.unseen) that is ...

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Is there a detailed explanation on why multiple population sampling distributions use difference for mean and proportion, while ratio for variances?
3 votes

The simple answer is because we have known distributions for those quantities. We generally believe differences of means and proportions should be asymptotically normal (and probably close to normal ...

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How to deal with interactions between fixed predictors when designing linear mixed effects models in R?
2 votes

There is no clear answer. If there is a theoretical reason to expect an interaction (or testing for one is important), then try out an interaction. For example: I hope people researching allergy ...

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If there are 40 candidate predictors, and I want to know which ones predict the dependent variable and in what way, is LASSO a good option?
2 votes

Not necessarily. Search around on feature selection and model selection. Model selection is not a solved problem and it is unlikely to be solved since it is NP-hard. In my own experience, I have seen ...

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What's a good resource for learning about applying linear regression to practical problems?
2 votes

I suspect you will get lots of opinions here since a good introductory text is a subjective ask. That said, you might want to look at something like Weisberg's Applied Linear Regression. That is used ...

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Correlated data series with single repeated value with a few outliers
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2 votes

I think there are a few ways you could look at your data. On the one hand, you have a dataset that is almost always right-censored. You could try to model the maximum MWh output if the plant were not ...

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Are there any models that need all data in memory for training?
2 votes

Random effects models require having all of the data in memory for most estimation methods apart from ANOVA-based estimators. Historically, ANOVA-based estimators were used when calculations were done ...

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Feature Selection in Multivariate Linear Regression
2 votes

A "Hard" Problem There does not exist a "best way" to select the variables in your model. If you have $p$ possible covariates, you get $2^p$ possible models without any ...

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Normalization of financial price to use as input in a neural network
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2 votes

Financial prices are, in general, not stationary. However, for a number of theoretical and empirical reasons we do think that log-returns (differences of $\log($prices$)$) are closer to stationary. ...

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indicator function in objective function with $L_2$ norm
2 votes

This problem is quickly and easily solvable if you split up the regions into four pieces: $x_0\geq a \cap x_n\leq b$: Solve $\arg\min ||\mathbb{A}x-b||^2 + \text{other linear least squares terms}$ $...

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Eigenvalues from `prcomp`
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2 votes

No, those are just eigenvectors. You need to save the output of prcomp into a variable and then look at the sdev component of that variable. Squaring the sdev component gets you the eigenvalues.

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Transforming dependent and independent variables with different techniques
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2 votes

There are indeed data-informed ways to transform the independent variables; however, they seem to have become a bit more obscure. You can indeed investigate using a Box-Cox transformation for your ...

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Why are my bootstrap confidence intervals for regression coefficients consistently wider than standard confidence intervals?
2 votes

This can happen when your data are not independent but instead have some dependence structure. For example, consider homes from across the country with some being in large expensive cities while some ...

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Seeking recommended literature search terms for a solution to a specific kind of data structure?
2 votes

The comments on blind source separation and independent components analysis are good. However, from what you have said, there might be an easier way. You said you have a sample of the pure noise ...

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Time Series Multivariate Forecasting
2 votes

Feature Selection Feature selection aka model selection is difficult. By that I mean it is an unsolved problem and there is evidence that it is an NP-hard problem. The title of Maymin (2011) hints at ...

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Paired vs Unpaired t-Test basics
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2 votes

In general, you would use a paired $t$-test when there is variation among observations which is shared (and matchable) between the two samples. So, in your example #1, yes: use a paired $t$-test since ...

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How to get a measure for the average "frequency" for wave-like data that changes frequency constantly over time?
2 votes

You just need to do a frequency decomposition of your data. The fft command in $R$ should get you what you want. The more difficult question is how to address variations in that frequency to determine ...

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Combination of distributions [reference request]
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2 votes

The term you are looking for is a mixture distribution. Mixture distributions get used in situations when: the observations involve a response to a choice (latent variable models), the data ...

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what should I do about a non-stationary variable in a panel-data interaction?
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2 votes

I think there are some ways to better express your data that might be helpful and avoid the issues of nonstationarity as well as some other issues you have not mentioned. You have measured stocks and ...

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Seasonality in data
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2 votes

A lack of seasonality at the monthly level need not imply a lack of seasonality at the weekly level. Layoffs may tend to happen at the beginning of the month after missing the prior month's targets. ...

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Interpreting group-level random effects of a multilevel model
2 votes

I believe that what you are getting is not exactly correct. You get the fit correctly and this includes BLUPs (best unbiased linear predictors = estimated random effects for a given level). From my ...

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Am I okay in not using EC model when series are co-integrated?
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2 votes

What you have given is the same as the Johansen long-run VECM for a VAR(1) model. So you should be able to estimate your top linear model directly. (Do be careful, however, about violations of ...

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