# Questions tagged [delta-method]

"The delta method, in its essence, expands a function of a random variable about its mean, usually with a one-step Taylor approximation, and then takes the variance." The term also refers to a method for showing that a function of an asymptotically normal statistical estimator is asymptotically normal.

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### How Best to Use the Delta Method to Approximate True Variance in a T-test Given Correlated Data?

Let's say that the analytical infrastructure at my place of work heavily centers around t-tests. I'd like to use this platform to perform a t-test on correlated data, e.g. the extent to which an order ...
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### Computing and simulating average marginal effect standard error using Delta Method with reproducible codes

I am trying to simulate calculating Average Marginal Effects on a basic linear regression with interaction on a binary variable and compare the empirical standard deviation I get from simulations and ...
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### How to use the delta method with a feols regression?

I have the following regression in R using the 'fixest' package. Yields are a function of N, N^2, P, K and S with producer by year fixed effects. ...
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### is ab test valid for concluding causal relation, when analysis unit differs from randomization unit?

In a typical A/B test, the randomization unit is user level, sometimes the analysis unit may be page/visit level, like a cluster randomization experiment. In this situation, the iid assumption doesn't ...
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### How to correctly estimate the ratio different of lower grain unit metric in Cluster randomized experiment?

I work on Education tech products that teachers/students would use in their learning journey. When we run experiment to test hypothesis of a feature, we need to do cluster randomization (cluster = ...
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### Delta Method to calculate the standard error of ratio in an AB testing context

In AB testing context, if we have a control group and test group (2 groups), and I'd like to calculate the relative difference (Mean test/ Mean control -1) and the confidence interval of this ratio ...
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### How to construct a confidence interval from a delta method approximation for the variance?

If I have a complicated function of multivariables $f(x_1,x_2,x_3,\ldots,x_n)$, and I were to find the variance approximation through the delta method, say $\sigma^2_{approx}$, would the 95% ...
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### Using the Delta Method to get confidence intervals for a function of a parameter

I'm trying to use the Delta Method to get a confidence interval on some function of a population parameter $\theta$. Suppose we want a 95% confidence interval on $\frac{1}{\theta}$, where we're given ...
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### When should I use the delta method rather than the parametric bootstrap?

Suppose I am willing to assume a particular likelihood function for an applied statistics problem. I am able to derive the MLE for the parameter $\theta$, which I will call $\hat{\theta}$. I can also ...
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### Delta method for $\bar X$^2

I have a question about the delta method. The question is: $X_1,...,X_n \sim N(\mu,\sigma^2)$, where $\sigma^2=V(x)$ and $\mu=E(X)$ let T=$\bar X^2$ be an estimate for $\mu^2$. Find the asymptotic ...
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### Derivation covariance between ratio of random variables

Suppose I am interested in computing the covariance between $\frac{A}{B}$ and $\frac{X}{Y}$. From Ratio of correlated vectors is uncorrelated? I understood that using the delta method, this amounts to ...
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### Calculating the variance of a function which depends on the standard deviation and mean of a random variable

I am a bit new to statistics and had some conceptual questions regarding the calculation of variance. I want to calculate the variance of a function $y=\frac{\sigma_{X}}{g(\overline{X})}$. As seen in ...
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### Stata vs. R: Delta Method provides different results for relative risk SE's from logit model

I've been trying to estimate the conditional mean treatment effect of covariates in a logit regression (using relative-risk) along with their standard errors for inference purposes. The delta method ...
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### Delta Method around zero is a N(0, 0)

I have this problem: $\sqrt N \hat{\theta} \sim N(0, V)$ where $E(\hat{\theta}) = \theta_{0} = 0$. I must find the asymthotic distribution of $\frac{N}{V}\hat{\theta}^{2}$ but if I use the Delta ...
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### Do I need delta method for calculating SE of absolute difference between two proportions?

I want to know if I need delta method for the below 3 scenarios for online experiment: % change of clicks per user between control and test group, (test clicks per user - control clicks per user)/...
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### Delta Method and Asymptotic Variance [duplicate]

I am working through a statistics course right now and struggling a lot with this question. I'm not really sure where to begin. Any reading or idea where I should begin? I really need to understand ...
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### Confidence Interval for Estimator using Delta method

The statement I am given the following discrete distribution with $\theta>0$ $$p(x) = \left(\frac{\theta}{1+\theta}\right) ^{2-x}\left(\frac{1}{1+\theta}\right)^{x-1} \hspace{1cm} x=1,2$$ I need to ...
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### Question about delta method and variance-stabilization

The delta method or variance-stabilizing transformation can be applied to make the variance be "nearly constant" (https://en.wikipedia.org/wiki/Variance-stabilizing_transformation). They use ...
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### How can the square of an asymptotically normal variable also be asympotically normal?

The Delta method states that, given $$\sqrt{n} (X_n - \mu) \xrightarrow{d} N(0, 1)$$ then $$\sqrt{n} (g(X_n) - g(\mu)) \xrightarrow{d} N(0, g'(\mu))$$ I'm surprised that this can be true. As a ...
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I have a logistic regression as follows: $\log \frac{p}{1-p} = \beta_0 + \beta_1x$. I'm looking for a confidence interval around a value of $x$, which would correspond to a specific value of $p$. ...