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 calculate confidence interval using the delta method in R?
I'm trying (struggling) to calculate the delta method for a confidence method in R. Does anyone know how to do it? Any advice would be most welcome.
In the literature, there's a simple IV/2SLS model ...
Sam
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Delta method vs actual expectation
If $x \sim N(\mu,\sigma^2)$, then by first principles,
$$\mathbb{E}(e^x) = e^{\mu + \sigma^2 / 2}.$$
I am trying to figure out where the "Delta method" is wrong here: If $(x-\mu) \sim N(0,\...
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Derive the expectation and variance of squared sample correlation: delta-method or else?
I would like to obtain the expectation and variance of the squared Pearson sample correlation ($\operatorname{E}(R_{lk}^2)$ and $V(R_{lk}^2)$) between two random variables $l$ and $k$ following a ...
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Understanding Asymptotic Relative Efficiency and how to compute it
I am learning about asymptotic relative efficiency (ARE) in class, and I am trying to understand exactly how to compute the ARE. From my understanding, asymptotic relative efficiency refers to ...
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A test of the difference between two r-squared?
According to Olkin and Finn (1995) and Alf and Graf (1999), the variance of the difference in r-squared is
$$
var(r_1^2 - r_2^2) = a \phi a^\mathsf{T},
$$
where $a = \begin{bmatrix}2 r_{1} & -2 r_{...
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Coefficient covariance matrix of inverse probability weighted regression
I am interested in computing an estimate $\hat\Sigma_\hat\beta$ of the asymptotic covariance matrix of the parameter estimates $\hat\beta$ in a regression of $Y$ on $\{X, Z\}$, weighted by weighs $\...
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Creating a confidence interval for the natural log of the proportion of successes [duplicate]
In a random sample of n subjects with n being very large, let X be the number of successes. Now I want to create the confidence interval for the natural log of the proportion of successes. Can I ...
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Reparameterization of the variance-covariance matrix (`apVar`) of the random-effect parameters estimated by `lme`
The question is about computing the variance of the random-effect parameters
estimated when fitting a linear mixed-effect model when the parameterization
of the random-effect parameters changes. This ...
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Reference needed for Delta method
I came to know from somewhere that there is a technique called delta method which can be used to approximate the distribution of a function of a random variable using the distribution of the ...
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Use the delta method to find confidence intervals
Given $X_1 ... X_n \sim \textrm{Exp}(\lambda)$, I found the MLE : $$\hat{\lambda} = \frac{1}{\bar{X}}$$
Now I need to find confidence intervals for: $$\eta = \lambda \cdot \log(\lambda)$$
To do so, I ...
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Estimating covariance based on Delta approach
I have a bivariate normal distribution $\left(X_1, X_2\right)$ with mean vector $\left(\mu_1, \mu_2\right)$ and some VCV matrix ...
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Delta method for ratio metrics
I have the following issue: I would like to do a power analysis (find the right sample size) for a ratio metric ($Z = \frac{X}{Y}$). The in-house statistical software I inherited uses a delta ...
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Deriving the asymptotic distribution using delta method
I have the density function:
$P_Y(y) = \sqrt{\frac{1}{2\pi y^3}} \exp\left(-\frac{(y-\mu)^2}{2\mu^2y}\right)$
If we define $r := \mu^2$ what is its asymptotic distribution?
The right answer is $\sqrt{...
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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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