Questions tagged [delta-method]

Question 1

What are some nice, insightful applications of the delta method? From Casella & Berger's Statistical Inference book (2nd ed.), the following example appears under The Delta Method: Example 5.5.19 ...

Question 2

Suppose we have a random variable $\hat \theta_n$ such that $\hat \theta_n \to \theta_0$ in probability. Let $f \colon \mathbb{R} \to \mathbb{R}$ be infinitely differentiable function. Then, the delta ...

Question 3

Let $( X_1, X_2, \dots )$ be independent and identically distributed random variables. Denote $(\mu = \mathbb{E}[X_i])$ and $(\bar{X}_n = \frac{1}{n} \sum_{i=1}^{n} X_i)$. Assume that $( \mu = 0)$ and ...

Question 4

Let $Y_n$ be a sequence of random variables with $\chi^2_n$ distribution. Using Slutsky' theorem or delta method prove that $$\sqrt{2Y_n}-\sqrt{2n-1}\stackrel{D}\to N(0,1)$$ In the first place I ...

Question 5

I'm working on a research internship about the precision of consumption price indexes and face some probems that leads me to ask a lot of questions about the methods I used and need to be answered. ...

Question 6

I would like to obtain the expectation and variance of the squared sample correlation ($\operatorname{E}(R_{lk}^2)$ and $V(R_{lk}^2)$) between two random variables $l$ and $k$ following a bivariate ...

Question 7

I have the following task: Let $Y$ be a binomial random variable. Find the asymptotic distribution of the ML estimate and find the asymptotic distribution of the estimator $(p(1-p))^{\frac{1}{2}}$ of ...

Question 8

EDIT In physics, most of us learned that \begin{align} \int_{a^-}^{a^+} f(x)\delta (x-a)dx&=f(a)\\ \frac{dH(x)}{dx}&=\delta(x). \end{align} So, would it be natural to have the below? \begin{...

Question 9

I want to understand this and the step that I'm struggling with is that apparently $$ \frac{1}{2\pi} \int_{-\infty}^\infty \exp \left (i k x \right) \text{d}k = \delta\left(x\right) $$ with $\delta$ ...

Question 10

So I understand that the delta method allows us to approximate the expectation and variance of a random variable. Mathematically, Let $Z = g(X,Y)$ where $X$ and $Y$ are random variables with $E[X] = \...

Question 11

Suppose X1, . . . , Xn are independent and exponential with parameter θ. Let p me an estimator such that p = #{i : Xi > 1}/n Where #A is the number of of elements in A. The original question is to ...

Question 12

I got a following setup: $(X_i)_{i \geq 1}$ are iid random variables with values in $\mathbb{R}$ and finite second moment. By the weak law of large numbers: $\sqrt{n}(\bar{X} - E(X))$ converges in ...

Question 13

Given $X_1,...,X_n \sim Gamma(\alpha,1/\alpha)$ random variables for some $\alpha>0$, let $\hat{\alpha}$ be a consistent estimator of the sample average $\bar{X}_{n}$ of the sample in terms of $\...

Question 14

Suppose there are two independent sequences of Bernoulli Random Variables $\{X_i\}_{1}^{n}$ and $\{Y_i\}_{1}^{n}$ with $P(X_i=1)=p_1$ and $P(Y_i=1)=p_2$. Let $\hat{p_1} = \frac{\sum_{i=1}^{n} X_i}{n}$ ...

Question 15

I have 7 variables $A_i$, $i\in\{-3,-2,-1,0,1,2,3\}$. ($A_{-1}$ and $A_1$) are identically distributed. ($A_{-2}$ and $A_2$) are identically distributed. ($A_{-3}$ and $A_{3}$) are identically ...

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Questions tagged [delta-method]

Conceptually Interesting Applications of the Delta Method [closed]

Delta method measurbility question.

Convergence of $( n^{3/2} (\bar{X}_n)^2)$ in distribution

Using CLT, Slutsky's theorem and delta method

Expectation of the inverse of an estimator using delta method linearization

Expected and Variance of the Squared Sample Correlation

Asymptotic distribution of estimator of the estimator of the standard deviation

How to fully understand the definite integral of a Dirac Delta function?

Why is $\frac{1}{2\pi} \int_{-\infty}^\infty \exp \left (i k x \right) \text{d}k = \delta\left(x\right)$? [duplicate]

How to put the bivariate/multivariate delta method into linear algebra notation?

Finding the asymptotic variance of an estimator

4th moment of the sample mean estimator

Asymptotic variance of a consistent estimator of gamma random variables

Asymptotic distribution of $T= \frac{\hat{p_2}-\hat{p_1}}{\sqrt{\frac{2 \hat{p} \hat{q}}{n}}}$

Covariance of normalized variables

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