4 votes
Accepted

Is the smooth transformation of an asymptotically efficient estimator still asymptotically efficient?

Refer to the lecture notes here (page 6 specifically) by Shao. Assume certain regularity conditions imposed on the distribution parameterized by $\theta$, so that the information matrix $I(\theta)$ is ...
StubbornAtom's user avatar
  • 11.1k
3 votes

Convergence in probability with double limits

Maybe I found the solution in the following Appendix on DOUBLE ASYMPTOTICS See equation C.9 Therefore it is sufficient that $m/n$ (or $n/m$) converges to a constant to ensure the double asymptotic ...
Almostsurely's user avatar
3 votes
Accepted

Linear regression with one generated regressor

The claimed equation is not true. Or, $\sqrt{n}(\widehat{\beta}-\beta_0)$ and $\sqrt{n}(\widetilde{\beta}-\beta_0)$ is not asymptotically equivalent. To see it, note that $\frac{1}{n}\sum_{i=1}^{n}\...
ExcitedSnail's user avatar
  • 2,748
2 votes
Accepted

How to calculate covariance matrix properly using Bartlett's formula

A few days more research and I finally found the answer. With large sample size ($n$) this equation gives a good aproximation to $C_{m\times m}$ (with $m < n$ as an arbitrary value). There is a ...
Erdem Şen's user avatar
2 votes

Do these two random variables have the same asymptotic distribution?

Assume that the $X_k$'s are jointly independent and identically distributed (with zero mean), so are the $W_k$'s (with mean equal to unity and variance equal to unity as are the premises), and they ...
Alecos Papadopoulos's user avatar
2 votes
Accepted

Do these two random variables have the same asymptotic distribution?

In general, no. For example, suppose $A_k$ are iid $N(0,1)$ and $B_k$ are also iid $N(0,1)$ and $X_{2k}=A_k+B_k$, $X_{2k+1}= A_k-B_k$. Then the $B_k$ all cancel and $$\bar Y_{2k}= \frac{2}{\sqrt{2k}}\...
Thomas Lumley's user avatar
2 votes
Accepted

Is the MLE variance estimator for the normal distribution asymptotically normal?

I think I understand now what your concern is. Let's take $X_i\stackrel{_\text{iid}}{\sim}N(\mu,\sigma^2),\,i=1,2,...,n$ The MLE of $\sigma^2$, $s_n^2$ is $\frac{n-1}{n}$ times the usual unbiased ...
Glen_b's user avatar
  • 282k
1 vote

Mixed Model in a repeated measurement design and AUC

Even with asymptotic normality among estimates of AUC* values, you might be better off using bootstrapping to estimate the precision and bias of your AUC estimates. Furthermore, depending on how you ...
EdM's user avatar
  • 92k
1 vote

Variance of sample moments - clarification on Serfling (1980)

Posting questions on CV has this magic effect many times: a little after you post them, you find the answer. ANSWER: both expressions are correct, and the expression in Theorem B holds also for the ...
Alecos Papadopoulos's user avatar
1 vote
Accepted

variance of an autoregressive process

"Then the sequence of partial sums $\{\sum_{r=1}^{a_n-1} c(kr)\}_{n\in\mathbb{N}}$ is a subsequence of $\{\sum_{r=1}^{n-1} c(r)\}_{n\in\mathbb{N}}$"---this statement is not correct. Your final result ...
Michael's user avatar
  • 3,328

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