# Questions tagged [standard-error]

Refers to the standard deviation of the sampling distribution of a statistic calculated from a sample. Standard errors are often required when forming confidence intervals or testing hypotheses about the population from which the statistic was sampled.

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### Can I use bootstrap results at the observation level?

I have read quite a bit of bootstrapping, but the issue I want to address seem not to appear. Consider a simple regression model: $$y_{i} = \beta_{0} + \beta_{1}x_{i} + e_{i}$$ I am aware that ...
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### Computing Standard Errors in EM algorithm

I'm applying the EM to a hidden markov chain (the $\mathbf{Z}=\{Z_1,...,Z_n\}$ variable), with observations(the $\mathbf{Y}=\{Y_0,...,Y_n\}$ variable) dependent not only on the hidden markov chain, ...
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### Standard Error of the cumulative value for time series

I have two time series, as in the picture below. The data was gathered experimentally. A practical example could be a measured mass flow rate, where I measure the mass flow rate over a certain time ...
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### Standard error for rolling regression

I am reading this paper: "The price of sin: the effect of social norms on market" In this paper, on the top of page 29: A reports the average coefficients obtained from the time-series regressions ...
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### Adjusting Standard Error for Imputed/Generated Regressors

This is my first question, so I hope this is a valid question. I am surprised that I have seen only few questions (and no answer helping me out) referring to the adjustment of variance estimators in ...
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### Which standard deviation of the cross-validation score?

When doing cross-validation for model selection, I found there are many ways to quote the "standard deviation" for the cross-validation scores (here "score" means an evaluation metric e.g. accuracy, ...
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### Aggregating Standard Errors for Predicted Probability Estimates

I obtain predicted values from a logistic regression for a certain outcome (e.g., mortality) at the hospital level – the data is at the patient level – and need to compute the average across hospitals....
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### Can I add a random effect accounting for huge differences within one factor?

The Experiment and Data The experiment I am working on has the following design: A B C D E F B A D E F C A B E F C D B A F C D E Each Letter represents a different level of ...
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### How to calculate the standard error of the mean for circular data?

I followed the suggestions here to calculate the SD from circular data in the R circular package: How to calculate standard deviation of circular data However, I need the SE of the mean for a number ...
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### Is the algorithm of calculating SEs of beta coefficients calculated by the nlme gls finally fixed?

I can read here: https://www4.stat.ncsu.edu/~davidian/st732/examples/dental_pa.R and here: https://math.unm.edu/~luyan/stat57918/week14.pdf that: WARNING: There is a MISTAKE in gls(), and it DOES ...
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### Standard error of the coefficient in GLM

I'm trying to learn about Wald test. I know, that its test statistics is $$t = \frac{\beta_i}{se\left( \beta_i \right)}$$ But, how is standard error $se$ computed in GLM? I've found only the ...
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### when can I substitute an inverse with a pseudo-inverse in an estimator

Short Version: can I substitute the Moore-Penrose generalized inverse of a matrix (R function ginv()) for a matrix inverse (R function ...
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### Statistical error for kernel density estimator

First of all sorry to use the word "error" without additional specification. I have a dataset with few elements ~(10-100) and I want to show them using a KDE (instead of simple histogram, for ...
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### How do you calculate the standard error of $R^2$

I would like to confirm something. I know that $R^2$ (in a linear regression) can be found by taking the square of Pearson's $r$. The standard error of Pearson's $r$ is calculated using the ...
527 views

### Caclulating standard errors for generalized least squares without raw data (just sample means and covariance)

I have a question very similar to the question asked here: is it possible to calculate standard errors (specifically, the standard error of the intercept) for generalized least squares regression ...
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### OLS standard error that corrects for autocorrelation but not heteroskedasticity

Question: By mapping the OLS regression into the GMM framework, write the formula for the standard error of the OLS regression coefficients that corrects for autocorrelation but not heteroskedasticity....
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### Significance of average correlation coefficients

I am using fMRI data (n=25) to predict performance on a behavioral task. At each of 12 time points, I train a linear model on data from n-1 subjects and use this model to predict the left-out subject'...
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### How to calculate standard errors of a non-linear model prediction?

I'm trying to understand how to show the prediction error of a model fit in R using the non-linear least squares function nls. Although there is an argument ...
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### Should the mean of the bootstrapped distribution always be asymptotically equal to the sample estimate?

Suppose I bootstrap the distribution of the sample mean. Normally, one would use the mean of the bootstrapped distribution as point estimate of the parameter and the s.d. as its standard error. The ...
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### Confirming the detailed calcs for NPS Margin of error

Based on this very good post How can I calculate margin of error in a NPS (Net Promoter Score) result? I've pulled together the detailed calculations to perform the test for the generalised NPS ...
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### K-Fold Cross-Validation - Formula for Standard Errors

I've recently tried to understand and formalize the one-standard-error rule for model selection by means of cross-validation. However, unfortunately I found most of the descriptions of the CV standard ...
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### SEs in multivariate regression

To avoid confusion, my question refers to multivariate regression as multiple dependent variables for the same set of independent variables. As far as I understand (see e.g., this question), the ...
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### Wild cluster bootstrap after linear model with multiple fixed effects

I am running a linear model with multiple fixed effects. I suspect that there is spatial correlation in my data so I cluster the SEs (46 clusters). But I am worried that the standard errors generated ...
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### Why is the Neyman estimator for the variance of diff in means conservatively biased?

Numerous lecture slides and papers claim that the Neyman estimator for the variance of difference in means is conservatively biased (i.e., the estimate is larger than the true variance). I must be ...
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### Interpreting standard errors of linear regression with logged dependent variable

I'm running a linear regression with a logged dependent variable. This is the only variable in the model that is logged. For interpretation, I've exponentiated the coefficients, subtracted one, and ...
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### What is the estimate of $\mathrm{Var}\left(\frac{nM}{X}\right)$ where $X$ is hypergeometric?

Consider the classical capture-recapture method, where we are to estimate the number of deer (say) in a sanctuary. So a certain number of deer is captured, tagged and released. Then a random sample is ...
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### Should instruments always weakly increase standard errors?

In OLS, are standard error estimates using some instrument $z$, different from $x$ always weakly larger than standard errors when not using instruments? This has been discussed before: Why is the ...
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### standard error about the mean apply to other values?

Does the standard error (SE) estimate of the mean (SE = sigma/sqrt(n)) only apply to the mean, or can it be applied to any value in the fit normal distribution? For example, if estimated 95th ...
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### Error in Linear Regression Parameters: Using mean measurement vs. all measurements

I have a set of measurements y taken at 17 different values of x, with 50 repeated measurements at each value of x. They follow a simple linear relationship y = mx + c, and I am fitting the parameters ...
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### Inverse probability weighting (IPW): standard errors after weighting observations

When using propensity scores for inverse probability weighting (IPW) the standard errors for the parameters in the regression model may be affected. I have seen several examples of people using ...
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### Numerical Approxmation of standard errors for parameter estimation in the EM algorithm

Generally, when you want to compute standard errors for estimated parameters within the ML framework, one uses the diagonal elements of the observed information matrix. In for instance ...
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### How to calculate stnd error for sample proportion with finite population correction when N is a random variable?

A coworker in the health insurance field is pulling a random sample of patient charts who have attempted suicide for a standard government report. Every random sample requires manual chart review, ...
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### Sandwich Estimator in Maximum Likelihood Estimation of Logit

I am estimating a discrete choice model using mixed logit using Halton Draws. So everything is effectively done with MCMC. The code is written in MATLAB. I am using MATLAB's ...
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### How to calculate the standard error of an odds ratio from the standard error of two logits?

For example, given two logits and their standard errors: Logit = -3.1435, SE = 1.6847 Logit = -2.7581, SE = 0.9081 I can calculate the odds ratio to be exp(-2.7581 - -3.1435) = 1.47, but is there a ...
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### Finding standard error of beta coefficients in ridge regression using lambda

I need to get the standard errors of coefficients with Ridge Regression, by calculating the SE of the beta estimates after I choose the right lambda. ...
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### How to calculate 'weighted' pooled/composite statistics for two given groups given group statistics

I have two sets of independent samples from the same distribution. For each, I have calculated sample weighted mean (u1, u2) sample weighted std deviation (d1, d2) sample weighted std error (e1, e2) ...
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### Standard error computation with interaction term

I aimed at studying the effects of an exposure (E) on fetal growth estimated by repeated ultrasound measurements (n = 2 measures per participant in the following example). I used interaction terms of ...
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### Manually computing bootstrap standard errors in the linear regression setting

I have written an R script for obtaining bootstrapped standard errors in the linear regression setting. In practice, first in a model building step I select the final model to be applied at each ...
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### Constrained Least Squares: Variance-Covariance/Std. Error Estimation

I'm looking to obtain standard errors for constrained linear model estimation. I'd like to be able to estimate standard errors and confidence intervals for the coefficients of $\beta'$ estimated via: ...
In unconstrained optimization, covariance matrix $C$ is parameterized in terms of its Cholesky ($C=LL^\prime)$. In other words, the parameter vector $\theta$ involves elements of the lower triangular ...