# 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 to estimate the number of known words in a text

I would like to estimate the proportion of known words in a text from a sample of tested words, where a subject answers if they know the meaning or not, and the frequency of how often they appear in a ...
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### Negative variance with Delta Method in A/B test analysis?

I'm analyzing a ratio metric in the context of an A/B test (e.g. "Clicks / Impressions"). Since the randomization unit and analysis unit are different (users vs impressions), I'm applying ...
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### Variance stabilizing transformation for logistic regression

Question: Are there (known) variance stabilizing transformations for logistic regression? Backgound: As an M-estimator, logistic regression is asymptotically normal, under suitable regularity ...
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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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### 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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### 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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### Delta method for estimating a ratio involving variance and mean

Let $X$ be a binomial RV with parameters $(n,p)$. I am interested in the ratio given by $\hspace{5cm}\boxed{R=\frac{var[f(X)]}{\mu[f(X)](1-\mu[f(X)])}}$ where $\mu[f(X)]$ denotes the mean of $f(X)$. ...
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### Delta method for Poisson ratio

Let $X_1,...,X_n$ be drawn from $Pois(\lambda)$ and $Y_1,...,Y_n$ from $Pois(\theta)$. I would like to find the asymptotic distribution of $$\frac{\overline X}{\overline X + \overline Y }$$ using ...
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### Confusion about the delta method

I'm reading Statistical Models by A. C. Davison and I'm really confused by this section on the Delta method. It's not mentioned explicitly, but is $h(T_n)$ a consistent estimator of $h(\mu)$? In the ...
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### Method for obtaining an asymmetric confidence interval

I have an estimator $\hat{\theta}$=$\frac{XY}{Z}$ where $X$ and $Y$ are constants and $Z$ is a random variable. $Z$ ranges from [1, $Y$]. Further $Z$ $\rightarrow$ $Y$ in the limit (asymptotically), ...
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### Why is the delta method defined the way it is?

The delta method begins with the assumption of $\sqrt{n} \left[X_n - \theta\right] \stackrel{D}{\to} \mathcal{N}(0, \sigma^2)$. Why is this? Wouldn't it make more sense to start in the more familiar ...
### Trying to approximate $E[f(X)]$ - Woflram Alpha gives $E[f(X)] \approx \frac{1}{\sqrt{3}}$ but I get $E[f(X)] \approx 0$?
Let $X \sim \mathcal{N}(\mu_X,\sigma_X^2) = \mathcal{N}(0,1)$. Let $f(x) = e^{-x^2}$. I want to approximate $E[f(X)]$. Wolfram Alpha gives \begin{align} E[f(X)] \approx \frac{1}{\sqrt{3}}. \end{align} ...
In Casella Example 10.1.18, the author says it is not easy to calculate the mean of gamma distribution. It seems that we CAN use the easy way $\bar X=\frac{\sum X_i}n$, but the variance of the mean we ...