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WLLN for bootstrap means of stationary ergodic processes?

Answered in comments above It seems as though the answer should be yes. I would suggest writing $X_n$ as $Y_n+Z_n$ where $Y_n$ is $X_n$ if $|X_n|\le m(n)^{1/3}$ and 0 otherwise; similarly $Z_n$ is $...
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Probabilistic Taylor theorem for concave functions

If $g^{(4)}\le0$, then $$g(x)=\sum_{k=0}^3\frac{g^{(k)}(0)}{k!}\,x^k+\frac{x^4}4\, \int_0^1g^{(4)}(sx)(1-s)^3\,ds \le\sum_{k=0}^3\frac{g^{(k)}(0)}{k!}\,x^k$$ for real $x$. Replacing here $x$ by $X-\mu$...
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Behavior of F distribution quantile as degree of freedom varies

$\newcommand\al\alpha$If the $(1-\al)$-quantiles of $F_{n,m}$ were decreasing monotonically in $m$ for each $\al\in(0,1)$, the the corresponding cdf's -- say $G_{m,n}$ -- would be increasing pointwise ...
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Does the (normalized) product of two independent binomial variables converges in distribution to a normal variable?

$\newcommand{\R}{\mathbb R}\newcommand\ep\epsilon\newcommand\tsi{\tilde\sigma}$Yes, of course. This follows by the multivariate (here, bivariate) so-called delta method. Indeed, we may assume that \...
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Transforming two smooth densities to the same density

This is impossible if $f$ is injective, without further assumptions such as bijective, differentiable, etc. Let $Q_1,Q_2$ be probability measures on a measurable space $(\Omega, \mathcal{F})$, and ...
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4 votes
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CLT convergence rate for sum of uniforms (in TV distance)

$\newcommand\dee{\Delta_{\mathrm{TV}}}\newcommand{\vpi}{\varphi}$Let $f_n$ denote the pdf of \begin{equation*} S_n:=\sqrt{\frac3n} \sum_{i=1}^n X_i \end{equation*} and let $\vpi$ denote the ...

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