# 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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### Using delta method (deviation of transformed variable)

How can in prove the following statement with delta method: "If I divide a variable by its deviation, the deviation of the transformed variable is 1."
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### How can I construct a confidence interval for the age dependency ratio?

Say I have a simple random sample of people from a given country, and I estimate the elderly dependency ratio in the population by taking the ratio of the number of people aged 65+ over the number ...
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### standard errors when bootstrap is not possible. delta method?

I run standard fixed effects regressions on a panel of aggregate firm level data (variables like average value added, average labor). I use the fixed effects that I estimate to simulate firm level ...
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### Asymptotic distribution of $\sqrt{n}\left(\hat{\sigma_{1}^{2}}-\sigma^2\right)$

I'm trying to find a confidence interval for variance $\sigma^{2}$ when some sample $X_{1},...,X_{n}$, with mean $\mu$ known, may have violated normality assumption. To do this I'm investigating the ...
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### Resampling-based Confidence Intervals for RERI

Relative Excess Risk Due to Interaction (RERI) has been used to quantify the joint effects of 2 exposures in epidemiology. RERI is the proportion of disease among those with both exposures that is ...
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### 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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I am interested in proving the delta method, where we show that $$\sqrt{n}(g(Y_n) - g(\theta)) \overset{\text{Dist}}{\to} \text{N}(0, \sigma^2 g'(\theta)^2).$$ We use Taylor expansion where $$g(Y_n)... 0answers 61 views ### Are the Inverses of two asymptotically equivalent matrices themselves asymptotically equivalent Suppose M_n = P_n + op(1). Is it the case that M_n^{-1} = P_n^{-1} + op(1), if both M_n^{-1} and P_n^{-1} exist with probability going to 1 as n increases? Can the Continuous Mapping ... 1answer 392 views ### Implicit hypothesis testing: mean greater than variance and Delta Method I am struggling with a hypothesis test between the mean and variance of a sample of i.i.d Gaussian random variables. This (self-study) question arises in the context of the Delta Method (first or ... 1answer 197 views ### Is the t-value (or z-value) of the margins of a logit model equal to the t-value of the coefficient? The accepted answer of this question seems to indicate that the z-value of the margin is the same as the z-value of the coefficient in the logit model. This, it seems, is true with how Stata ... 1answer 249 views ### Estimator for Pareto Distribution & Delta Method Assume that Y has a Pareto distribution with parameters (\theta, t = 1). An estimator of \theta is \tilde{\theta} where \bar{Y} = \frac{\tilde{\theta}t}{\tilde{\theta} - 1}. Solve for \... 1answer 349 views ### Degrees of freedom for t-test after delta method Say I have a dataset with n observations of two independent variables, X and Y. From the observations of the X variable I estimate a parameter \hat{\alpha} and corresponding variance \hat{\sigma}... 0answers 21 views ### Showing p-th sample quantile is asymptotically normal [duplicate] I'm working through van der Vaart to improve my knowledge on asymptotic statistics, and I'm attempting the following problem. Let F_n^{-1}(p) be the p-th sample quantile of a sample from a ... 0answers 255 views ### Why is delta method only for asymptotic distributions? I'm wondering why the delta method, , "is only used for asymptotic distributions", as @mpiktas write in this post: Variance of a function of one random variable, or as is written here: "The delta ... 1answer 329 views ### Standard error of the estimate in logistic regression We usually get an estimate of \beta in the logistic regression by finding the MLE of the observed random samples of X_1,X_2....,X_N. Then we use Wald's test i.e. {[\hat \beta / S.E.(\hat \beta)]... 0answers 109 views ### Higher order delta / taylor series approximation relationship to normal distribution? For a normally distributed variable X, one can call on the delta method to provide an asymptotically normally distributed variable for a non-linear function of it, g(X). This is based on a linear ... 1answer 413 views ### Delta Method Confidence Intervals In a standard linear regression setup:$$ y_t = \beta X + \varepsilon _t$$where$$ e_t \sim N(0, \sigma ^{2}) $$I have found the Maximum Likelihood Estimators for β and σ (from OLS), but now ... 1answer 246 views ### Delta Method with Ratio that Cancels Say I have Gas Consumption = Energy Used Per Hour * Heating Hours and I want to construct a CI for Gas consumption. Do I have to use the delta method and write:$$\mathrm{Var}(GC) = \mathbb{E}(\...
Given a probability density say $f(x)$ with parameters $\theta$ and a sample of size n say $x_1,\ldots,x_n$ we can compute the MLE estimate say $\theta_n$ by passing $f$ and $x_1,\dots,x_n$ to ...