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Results tagged with mathematical-statistics
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user 53438
Mathematical theory of statistics, concerned with formal definitions and general results.
6
votes
1
answer
238
views
Asymptotic joint distribution of the sample medians of a collection and a sub-collection of ...
Let $X_1,\dots, X_n$ denote i.i.d. random variables, with a smooth density $f$ having unique median $m$.
It is known that the sample median $M_n$ of $X_1,\dots, X_n$, $M_n = \operatorname{med}(X_1, \ …
- 722
5
votes
Accepted
How to derive the asymptotic distribution of the test statistic of a large sample test for e...
The OP is correct that you just cannot "add" convergence in distribution, for this you have to be aware of the covariance structure, which is fortunately enough trivial in this case.
update: Thanks f …
- 722
0
votes
Convergence in probability in high-dimensional settings
I assume that the dependence on $n$ is through $\hat \theta = \hat \theta_n$, and that $\theta$ is fixed.
Let $\varepsilon > 0$ and $\gamma > 0$. Let $F_n$ be the distribution function of $n \|\hat …
- 722