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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69 views

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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605 views

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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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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669 views

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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953 views

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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2k views

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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178 views

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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3k views

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 ...
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476 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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632 views

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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275 views

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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1k views

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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1k views

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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561 views

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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13 views

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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1answer
45 views

Standard error in multiple regression

I want to calculate standard error of y-intercept or constant term in the multiple regression equation $Y = b_0 + b_1X_1 + b_2X_2$ I found the formula for standard error estimation of co-efficient $...
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2answers
164 views

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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72 views

Should I use Student's t-distribution to evaluate my measurement's confidence interval?

I'm an experimental physicist who mainly needs statistics for the calculation of uncertainties/confidence intervals. Since my results are usually normally distributed, I simply take $N$ measurements ...
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37 views

Approximating standard error that contains a parameter, by replacing the parameter with its estimate

I am a bit confused about the following step I have seen in the stats literature which seems to me a bit circular. Say you are approximating the standard error of the MoM estimate of an exponential ...
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346 views

Delta Method Average Marginal Effects Multinomial Logit

Following the incredible demonstration in Statalist by Jeff Pitblado on how to calculate - using the Delta Method - the Standard Errors for Average Marginal Effects of a Logit Model. Q: What would ...
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121 views

My Tobit model gives all infinite standard deviations

I am trying to do a Tobit estimation (in R) because my dependent variable ranges from 0-100 with many values at a 100. ...
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95 views

Why don't we use the n-1 correction for standard error of sample proportion?

From my understanding, when we construct a confidence interval for a sample mean with a sample size of n, we try to estimate the standard deviation of the sampling distribution $$σ_{\overline{x}} = \...
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147 views

When modeling a rate using Poisson regression, how can I incorporate the standard error for the rate?

I have a data set with age-standardized mortality rates per 100,000—along with the standard error for the rate—for all US counties. I also have various predictors, and would like to use multilevel ...
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382 views

Estimating standard error of Monte Carlo integration, non-MCMC version

Let us suppose that we're to evaluate the expectation of a random variable $h$ with respect to some distribution $\pi$, $\text{E}_{\pi}[h]$. The standard Monte Carlo estimate, using a sample of $X_1, ...
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205 views

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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1answer
124 views

AUC variance for estimators with randomness (e.g. Random Forest)

I know that we can calculate the standard error for the AUC for all estimators, assuming that the conditional density is fixed. What I'd like to do, however, is additionally account for the randomness ...
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44 views

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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550 views

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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190 views

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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445 views

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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462 views

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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1k views

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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3k views

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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244 views

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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3k views

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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554 views

Standard error of estimates of covariance parameterized in tems of cholesky

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 ...
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68 views

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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21 views

Standard error clustering: Does it depend on the variable of interest?

Suppose I am interested in whether a students age affects their performance, and I run the following regression: $performance(i) = \beta_1 age(i) + \beta_2 Female(i)+\beta_3 classsize(i)+\varepsilon(...
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1answer
127 views

Formula to Calculate Confidence Interval of Marginal Means

What is the formula for the marginal means confidence interval in a regression analysis? Let us have the following regression $Y = b_0 + b_1X + b_2Z + b_3 XZ + b_4 Cov_1 + b_5 Cov_2$ If I get it ...
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27 views

Using standard error of estimate instead of mean in a t-test?

I am pretty new in the realm of statistics of testing differences. I do know the basic t-test that tests differences of means (or against that of null effect) in which we use standard error of the ...
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32 views

Calculating standard error of coefficients in segmented regression

Consider the following equation resulted from segmented regression: $$\hat y_i = \begin{cases} \hat\beta_1 x_i + (\hat\beta_0 - \hat\beta_1 \cdot c) &\text{if } x_i \le c \\ \hat\beta_2x_i + (\hat\...
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88 views

SAS and R gives different standard error when fitting Tweedie model

I would like to fit a Tweedie GLM to the data. However, even though PROC GENMOD from SAS and glm() from R gives the same coefficient estimates, they give quite different standard error. What it the ...
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47 views

Interpreting the margin of error when it is larger than the sampled proportion

Say that I have a population of $N=500$ individuals, and I'm sampling $n=60$ of them for a certain characteristic which is expected to be quite rare (say green eyes). In my sample I find out there are ...
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63 views

How to calculate the standard error of ratio of two AUC

Please can anyone help me with this! I hope my explanation is going to be simple: This is the data I have: I only have access to the aggregated data as below. the first column is the time points a ...
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0answers
87 views

Intuition behind White's Estimators/ Heteroscedasticity-consistent Standard Errors

For a medical study I am trying to understand the intuition behind heteroscedasticity-consistent standard errors. I know that it can be used, when in OLS regression residuals are heteroscedastic. By ...
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1answer
42 views

Standard error for sum of estimated parameters

A basic query. We are doing a meta analysis where we are gathering estimated relationships from a series of papers. Each of these studies estimates two parameters of interest say b1 and b2 and reports ...
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224 views

The link between error bars representing the standard error of the mean and statistical significance

I have read the following on many websites: What can you conclude when standard error bars do not overlap? When standard error (SE) bars do not overlap, you cannot be sure that the ...
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57 views

Why doesn't clustering bias the standard errors in this very simple simulation?

I simulate a very simple model with one regressor and a random intercept: $$y_{ij} = \beta_0 + \beta_1x_{1,ij} + u_j + \epsilon_{ij}$$ I run model <- lm(y ~ x1) ...
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124 views

Where does the standard error come from in Lasso?

I'm using Lasso to get the best variables to predict an outcome. I understand that this graph gives me λmin and λ1se However, I don't understand how to get that standard error theoretically. Where ...
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25 views

Estimated Standard Error of a Method of Moment Estimator, Poisson Example

For X randomly sampled from a Poisson(lambda) population, the method of moment estimate of lambda is the sample mean: lambda_hat = X_bar Now, say we are interested in the variance of lambda_hat (...