Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Inference with a Multidimensional Multiscale Statistic   We observe a stochastic process $Y$ on $[0,1]^d$ ($d\geq 1$) satisfying
$dY(t)=n^{1/2}f(t)dt$ + $dW(t)$, $t \in [0,1]^d$, where $n \geq 1$ is a given
scale parameter (`sample size'), $W$ is the standard Brownian sheet on
$[0,1]^d$ and $f \in L_1([0,1]^d)$ is the unknown function of interest. We
propose a multivariate multiscale statistic in this setting and prove its
almost sure finiteness; this extends the work of D\"umbgen and Spokoiny (2001)
who proposed the analogous statistic for $d=1$. We use the proposed multiscale
statistic to construct optimal tests for testing $f=0$ versus (i) appropriate
H\"{o}lder classes of functions, and (ii) alternatives of the form $f=\mu_n
\mathbb{I}_{B_n}$, where $B_n$ is an axis-aligned hyperrectangle in $[0,1]^d$
and $\mu_n \in \mathbb{R}$; $\mu_n$ and $B_n$ unknown. In the process we
generalize Theorem 6.1 of D\"umbgen and Spokoiny (2001) about stochastic
processes with sub-Gaussian increments on a pseudometric space, which is of
independent interest.

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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio