# Tagged Questions

"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 ...

49 views

### Why are confidence intervals computed by the delta method so uneven?

I plotted a treatment effect on some performance measure over the course of an experiment. Stata has a nice feature called margins and marginsplot to do this. So what I do is run a linear regression, ...
35 views

### Standard error of marginal effect for binary/categorical variable

The delta method/bootstrap method is used to obtain the standard error of marginal effect in case of limited dependent variable model (like tobit model). I have seen these being applied for the ...
96 views

### The vcov function cannot be applied?

I originally asked a question about the delta-method in the context of the hyperbolic distribution. I got an answer there, which is useful, except that it says I should apply the ...
193 views

### Standard errors of hyperbolic distribution estimates using delta-method?

I want to calculate the standard errors of a fitted hyperbolic distribution. In my notation the density is given by \begin{align*} ...
313 views

### Standard error of the quotient of two estimates (Wald estimators) using the delta method

I have two coefficients' estimates from a regression, each of which has an estimated standard error. I would like to know the quotient of these two estimates -- that is, divide one of the estimates by ...
50 views

### calculating variance of sum of predicted costs from two-part model

I have a question regarding the calculation of the variance of the sum of predicted health care costs using a two-part regression model. Details are below, but it boils down to how to calculate the ...
94 views

### Do I apply delta method correctly?

I'm no mathematician, so please consider the whole explanation as a subject to criticism and optimization. I'm trying to build a model and calculate an estimate of error variance for the following ...
81 views

### Approximate distribution of normal squared

I am studying for a test, one section of which will cover the delta method. This problem came from that section: Let $X\sim N(\mu,n^{-1})$. Find an approximate distribution of $X^2$. (It also asks ...
122 views

### Delta method in a multinomial logistic regression

I am estimating a multinomial logistic model with R (package "mlogit"). I use the estimated coefficients to get the estimated odds and then I apply the Delta Method (package "deltamethod") to get ...
130 views

### Delta Method Derivation

I at looking at Xu and Long's paper on using the delta method to construct CI's for logistic regression predicted probabilities. I am generally following except for two questions I am hoping someone ...
101 views

### Elementary approach to higher order asymptotics

I am trying to understand “higher order asymptotics”. I find several texts on Likelihood asymptotics, nothing’s easy to read... if you have any nice pointers on this direction, I’ll be interested; ...
73 views

### Can we approximate the distribution of S?

I want to understand how the sampling distribution of the whole covariance matrix behaves for large $n$. I am trying to use the delta method and multivariate CLT. I am trying to show that when the ...
273 views

### Can RSD be pooled or is it valid to use the uncertainty propagation rule?

This might be a strange case, but I'm sure that somebody in here can help me and that I'm perhaps not the only one who wants to pool RSDs correctly. Consider this: The mean weight of a powder bed is ...
287 views

### What is a “polynomially bounded” function, and why is this a requirement of the The Delta Method?

I am reading a paper "A note on the Delta Method" by Gary Oehlert, JASA, 1992. I am trying to estimate the variance of a function of a random variable, but first I want to understand the limitations ...
137 views

### How to describe variation on multiple levels?

This is continuation for a series of questions (1, 2). I have a data set from an experiment with 2x2 design. A replicate consists of 20-50 normally distributed replicate measurements. Each treatment ...
701 views

### Calculating the Variance using Delta Method

I'm trying to find the variance of $L$, $Var(L)$, using the delta method (I want to find a closed form). $L$ is defined as: $$L = \frac{A}{B} + \frac{C}{D}$$ All $A$, $B$, $C$, and $D$ are dependent. ...
136 views

### The mean and Variance of $log(Combination Index)$

In biological sciences, ($CI$) stands for the Combination Index which is a conventional method for dose-response assessment and drug interaction analysis. It can be defined as: CI = ...
567 views

### Delta method and correlated variables

I have been reading about the delta method in regards to auto regressive distributed lag models. This is very new to me, so excuse any beginner mistakes. The problem is as follows: We have a model ...
275 views

### How to compute asymptotic confidence intervals for differences in quantiles?

Can anyone give me advice on computing the asymptotic confidence intervals for a difference in quantiles of a distribution? For example, I have fit a log-normal distribution to doubly interval ...
230 views

### Power analysis for matched poisson variables

I have two matched groups consisting of 22 observations each for a Poisson distributed variable. I am interested in evaluating the power to detect a 20% decrease in the outcome for the second group. I ...
858 views

### How do you calculate standard errors for a transformation of the MLE?

I need to make inference about a positive parameter $p$. To acomodate the positiveness I reparametrized $p=\exp(q)$. Using MLE routine I computed point estimate and s.e for $q$. The invariance ...
Let $S_n = \frac{1}{n}\sum_{i=1}^n X_i$, and $T_n = \frac{1}{n}\sum_{j=1}^nY_i$, where The $X_i$ are iid, the $Y_i$ are iid (with a different law) $X_i$, and $Y_i$ are dependent For $i\neq j$, ...
Lets say we have random variable $X$ with known variance and mean. The question is: what is the variance of $f(X)$ for some given function f. The only general method that I'm aware of is the delta ...