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Why Does Standard Error for Individual Predictors Not Increase in Multilevel Modeling?

"Not doing multilevel modeling causes an underestimation of standard error" is an imprecise statement as it doesn't specify which standard error we underestimate if we ignore the ...
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Computing and simulating average marginal effect standard error using Delta Method with reproducible codes

One thing you are doing wrong is that you do not take the square root of result: you are comparing a variance with a standard deviation. The second thing, if I ...
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2 votes

Standard Errors for Numerical Optimization using Chi-Square Objective Function

There are various Chi-square minimization methods described in the literature. All of them boil down to minimizing a sum (or average) of normalized squared residuals (or Chi-square distances). The ...
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Should we always minimize squared deviations if we want to find the dependency of mean on features?

Yes, it is possible for estimators obtained by minimizing some different than squared deviation to give a better estimator of model parameters. The question of whether a given estimator can be beaten ...
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Should we always minimize squared deviations if we want to find the dependency of mean on features?

Your estimator is the OLS estimator in nonlinear regression Your problem is essentially just the OLS estimation problem in nonlinear regression. To see this, suppose you have nonlinear regression ...
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Should we always minimize squared deviations if we want to find the dependency of mean on features?

A similar question (if not the same) is: If the predicted value of machine learning method is E(y | x), why bother with different cost functions for y | x? The theoretical mean of a distribution ...
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1 vote

Should we always minimize squared deviations if we want to find the dependency of mean on features?

NO It is important to keep in mind that an estimator of a parameter can take on many forms. In fact, constants can be estimators! Consequently, we might find that calculating something other than the ...
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Should we always minimize squared deviations if we want to find the dependency of mean on features?

Can it be the case that a use of something different from squared deviation gives a better estimate of model parameters (for example more accurate (smaller width) and with smaller or no systematic ...
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7 votes

Should we always minimize squared deviations if we want to find the dependency of mean on features?

Minimizing the MSE in the cases you describe indeed produces a consistent estimator for the model parameters. The consistency is related to the fact that the derivative of the MSE, and therefore the ...
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Error bars on error bars?

TLDR; Below is a simulation where we repeated an experiment of estimating the mean of a normal distribution with $\mu = 0$ and $\sigma = 1$. We did 200 repetitions with samples of size 10. We can ...
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7 votes

Error bars on error bars?

The traditional design of error bars gives an unfortunate impression of some linear distribution of uncertainty, and places a lot of visual emphasis on the the end of the bar, which is where the ...
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Error bars on error bars?

You are interested in standard errors, which describe the variability in a parameter estimate, and are related to your sampling approach. This is distinct from the parameters themselves (e.g. mean and ...
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20 votes

Error bars on error bars?

The objects we use to make inferences (e.g., estimates, confidence intervals, error bars, test statistics, p-values, etc.) are statistics, meaning that they are functions of the observed data. Since ...
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4 votes

Error bars on error bars?

Review of confidence intervals Let $\theta \in \mathbb{R}$ be a parameter of interest which we study based on a random variable $X$. An exact $1-\alpha$ confidence interval $(L(X),U(X)$ is defined by ...
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Error bars on error bars?

The short answer is "no." However you construct your error bars, they are a rule. You cannot be unsure of them. Let us imagine that they are confidence intervals. There are multiple ...
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Interpreting standard error for dummy variables in linear regression models

The underlying math is that the intercept ($\beta_0$) indicates the average salary of men, in \$1000; the parameter $\beta_1$ indicates the difference between the average woman's and average man's ...
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1 vote

Bootstrap Standard Errors: should I divide the sampling standard deviation by $\sqrt{n}$?

The standard error of the mean, with its $\sqrt{n-1}$ in the denominator, is a particular closed form of the standard error (SE), obtained exactly for the mean as a considered statistic. For any ...
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For bivariate linear model, if the residuals ARE normal, but the data is NOT normal, can I make inferences about the slope coefficient?

Yes! The usual linear regression model does not assume that X is normal. The assumptions are independence, homoscedasticity, linearity and normality of residuals.
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