Questions tagged [asymptotic-covariance]

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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 ...
3
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1answer
276 views

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 $$...
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1answer
49 views

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 ...
1
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1answer
43 views

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 ...
1
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1answer
30 views

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 ...
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0answers
2k views

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 ...
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0answers
5 views

Implication of a kronecker product that is Martignale Difference Sequence

I have only come across the Kronecker product of two matrices in the past, and as such I find this equation that I have encountered in an Econometric Theory paper (surrounding sign-based inference) ...
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0answers
10 views

Estimating the asymptotic covariance matrix using Bartlett Kernels within a nonparametric test statistic framework

I am unsure whether this question best fits here or on Stackoverflow, as I am struggling to replicate the results of a paper on R. However, due to the statistical nature of the question, Stackexchange ...
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0answers
13 views

Can someone kindly explain the function asyCov which computes the asymptotic covariance matrix of a correlation/covariance matrix

Here is the link for more references on this particular function: https://www.rdocumentation.org/packages/metaSEM/versions/1.2.5/topics/asyCov I'm interested in obtaining the asymptotic covariance ...
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0answers
16 views

Can someone kindly explain how to obtain the sampling variance of 2 covariance in r

So basically, I’m currently modelling a 1-1-1 multilevel mediation from bauer et al., (2006). That is, it is a stacked mediation model, meaning that the mediation and outcome equation are stacked into ...
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0answers
9 views

How to proof the asymptotic properties of the penalized spline estimator using asymptotic notations?

Please could someone proof how the Average Mean Squared Error of penalized spline estimator is given as \begin{eqnarray} AMSE(\hat{l} )=\...
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1answer
131 views

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 ...