Questions tagged [asymptotic-covariance]
9 questions
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Variance of sample moments - clarification on Serfling (1980)
In "Serfling, R. J. (1980). Approximation theorems of mathematical statistics", we read
In Theorem A, as one suspects, $k=1,2,...$, indicating the integer-moments, while $n$ is the sample size. As regards the $m_k$ and $\mu_k$ symbols, we have,…
Alecos Papadopoulos
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variance of an autoregressive process
Let $\{x_t\}_{t\in\mathbb{N}}$ be a zero mean strictly stationary sequence of random variables and $c:\mathbb{N}\to\mathbb{R}$ the (auto)covariance function. If the process follows the AR(1) model
$$x_t=\rho x_{t-1}+e_t$$
with $e_t\sim…
Celine Harumi
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Variance of evidence lower bound(ELBO) loss function
When using Bayesian optimisation in a neural network our loss function is equal to:
Here the first term is the KL divergence between the approximate and true posteriors. The second term is the loglikelihood function.
I want to know how we can…
Onno Van Steen
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Do these two random variables have the same asymptotic distribution?
Let $\{X_k\}$ be a sequence of dependent random variables with mean 0. Define $\bar{Y}_k = \frac{1}{\sqrt k}\sum_{i=1}^k X_i$.
Let $\{W_k\}$ be a sequence of i.i.d. random variables with mean 1 and variance 1. Define $\bar{Z}_k = \frac{1}{\sqrt…
user3294195
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convergence of sample covariance matrix in case sample size depends on dimesion
Let $X_1,X_2,\dots,X_n$ be random sample from $\mathcal{N}_p(\mathbf{0},\mathbf{\Sigma})$ and put $\mathbf{S}=\frac{1}{n}\sum_{i=1}^nX_iX_i^t$, which is sample covariance matrix. If $p
BongJung
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Convergence in probability with double limits
Suppose you have a sequence of random variables $
\left\lbrace X_{i}\right\rbrace_{i=1,...,n}$ which converges in probability to a random variable $X$, shown by $ X_n \ \xrightarrow{p}\ X$ as n goes to $\infty$.
$$\lim_{n\rightarrow\infty}…
Almostsurely
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Linear regression with one generated regressor
Suppose I have the regression model: $Y_i=T^{\top}_{i}\beta_0+e_{i}$ with $E(e_i|X_i)=0$, where we have two regressors $X_i,\ E(D|X_{i})$ so that $T^{\top}_{i}=[X_i,\ E(D|X_{i})]$. $X_{i}$ is a discrete random variable with support $\{1,2,3\}$ and…
T34driver
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Mixed Model in a repeated measurement design and AUC
My goal is to predict the $Y_i=1$ for each subject $i$ given a set of explanatory variables $x_i$. Since I have repeated measurements for some subjects, I was told to use a mixed model strategy, i.e. I assume that $$\mathbb P(Y_i=1\mid x_i) =…
lmaosome
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OLS estimator of ARMA(1,1) process
When I solved the DGP in the picture, I got an ARMA(1,1) process with intercept term (1-a)*mu.
To solve my problem I need the (X'X)^-1(X'Y) form equation of "mu hat".
How can I derive the equation in this kind of situation??
(My problem is to find…
Park
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