# Questions tagged [asymptotics]

Asymptotic theory studies the properties of estimators and test statistics when the sample size approaches infinity.

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### Does the Bernstein von Mises theorem require that the true posterior is actually Gaussian?

Reading up on the Bernstein von Mises Theorem, it says that in the infinite data limit, the posterior converges to a Multivariate Gaussian. Just a sanity check which I cannot find anywhere...This is ...
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### Probability of correctly identifying the Bayes class

Consider $X$ being a random variable taking value $\{1, \ldots, K\}$, with probability $p_1 = \frac{1}{K} + \varepsilon$ and $p_k = \frac{1}{K} - \frac{\varepsilon}{K-1}$ for all $k \neq1$. Taking i.i....
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### Large sample properties of classical estimator for single scale parameter

This question was first posted on Math Stackexchange and I was told in the comment it would be a good question on Stats Stackexchange, since it comes from the well-established theory of point ...
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### Delta method for $\bar X$^2

I have a question about the delta method. The question is: $X_1,...,X_n \sim N(\mu,\sigma^2)$, where $\sigma^2=V(x)$ and $\mu=E(X)$ let T=$\bar X^2$ be an estimate for $\mu^2$. Find the asymptotic ...
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### Positive definiteness of integral of matrix

I was reading a paper, and did not understand a statement that the author made without further explanation. The author derives the limiting distribution of a non-linear least-squares estimator and ...
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### Question regarding asymptotic assumptions and hypotesis testing paradox for large samples

Suppose we would like to verify if a r.v $X$ follows a distribution with cumulative density as $F$, if $n$ goes to $\infty$ I'm able to use komogorov test which states reject $H_0$ (stating that $X$ ...
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### MLE of log-normal distribution with one parameter

Suppose we have a sample of random variables $X_1, \cdots, X_n$ that are from a log-normal distribution, where $\log X_i \sim N(\mu,\mu^2)$ (same variance and mean). Find the MLE $\tilde{\mu_n}$ of \$\...
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### is inverse of 1 + small op(1) equal to 1 + small op(1)?

One rule for small op and big Op is $$(1+o_p(1))^{-1} = O_p(1)$$ (on page 13 of Vaart, A. W. van der. (1998). Asymptotic statistics. Cambridge University Press.) I am curious whether it is true to ...
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1 vote
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### Bias of MLEs increases rather than decreases in n

In the context of conducting simulations to assess the performance of MLE point estimates for truncated data, I am encountering surprising settings in which the bias of MLEs is clearly non-monotonic ...
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