"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 ...
0
votes
0answers
21 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 ...
1
vote
0answers
53 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 ...
1
vote
1answer
55 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 ...
1
vote
0answers
78 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 ...
0
votes
0answers
102 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 ...
5
votes
1answer
76 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; ...
2
votes
0answers
72 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 ...
2
votes
0answers
178 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 ...
2
votes
0answers
207 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 ...
4
votes
1answer
117 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 ...
1
vote
1answer
544 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.
...
2
votes
0answers
125 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 =
...
2
votes
1answer
451 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 ...
6
votes
1answer
200 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 ...
4
votes
1answer
188 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 ...
3
votes
2answers
621 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 ...
6
votes
1answer
229 views
Limiting distribution of a squared sum of random variables
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 $i\neq j$, ...
10
votes
2answers
4k views
Variance of a function of one random variable
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 ...
