Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bump hunting with non-Gaussian kernels   It is well known that the number of modes of a kernel density estimator is
monotone nonincreasing in the bandwidth if the kernel is a Gaussian density.
There is numerical evidence of nonmonotonicity in the case of some non-Gaussian
kernels, but little additional information is available. The present paper
provides theoretical and numerical descriptions of the extent to which the
number of modes is a nonmonotone function of bandwidth in the case of general
compactly supported densities. Our results address popular kernels used in
practice, for example, the Epanechnikov, biweight and triweight kernels, and
show that in such cases nonmonotonicity is present with strictly positive
probability for all sample sizes n\geq3. In the Epanechnikov and biweight cases
the probability of nonmonotonicity equals 1 for all n\geq2. Nevertheless, in
spite of the prevalence of lack of monotonicity revealed by these results, it
is shown that the notion of a critical bandwidth (the smallest bandwidth above
which the number of modes is guaranteed to be monotone) is still well defined.
Moreover, just as in the Gaussian case, the critical bandwidth is of the same
size as the bandwidth that minimises mean squared error of the density
estimator. These theoretical results, and new numerical evidence, show that the
main effects of nonmonotonicity occur for relatively small bandwidths, and have
negligible impact on many aspects of bump hunting.

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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph