# On Asymptotic Minimaxity of Kernel-based Tests

ESAIM: Probability and Statistics (2010)

- Volume: 7, page 279-312
- ISSN: 1292-8100

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topErmakov, Michael. "On Asymptotic Minimaxity of Kernel-based Tests." ESAIM: Probability and Statistics 7 (2010): 279-312. <http://eudml.org/doc/104309>.

@article{Ermakov2010,

abstract = {
In the problem of signal detection
in Gaussian white noise
we show asymptotic minimaxity of kernel-based tests. The test statistics
equal L2-norms of kernel estimates.
The sets of alternatives are essentially nonparametric and are defined as
the sets of all signals such that the L2-norms of signal smoothed
by the kernels exceed some constants pε > 0.
The constant pε depends on the power ϵ
of noise and pε → 0 as ε → 0.
Similar statements are proved also if an additional information
on a signal smoothness is given.
By theorems on asymptotic equivalence of statistical experiments
these results are extended to the problems of testing nonparametric
hypotheses
on density and regression. The exact asymptotically minimax
lower bounds of type II error probabilities are pointed out for
all these settings. Similar results are also obtained for the problems
of testing parametric hypotheses versus nonparametric sets of alternatives.
},

author = {Ermakov, Michael},

journal = {ESAIM: Probability and Statistics},

keywords = {Nonparametric hypothesis testing;
kernel-based tests; goodness-of-fit tests; efficiency; asymptotic minimaxity;
kernel estimator.; kernel-based tests; kernel estimators},

language = {eng},

month = {3},

pages = {279-312},

publisher = {EDP Sciences},

title = {On Asymptotic Minimaxity of Kernel-based Tests},

url = {http://eudml.org/doc/104309},

volume = {7},

year = {2010},

}

TY - JOUR

AU - Ermakov, Michael

TI - On Asymptotic Minimaxity of Kernel-based Tests

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 7

SP - 279

EP - 312

AB -
In the problem of signal detection
in Gaussian white noise
we show asymptotic minimaxity of kernel-based tests. The test statistics
equal L2-norms of kernel estimates.
The sets of alternatives are essentially nonparametric and are defined as
the sets of all signals such that the L2-norms of signal smoothed
by the kernels exceed some constants pε > 0.
The constant pε depends on the power ϵ
of noise and pε → 0 as ε → 0.
Similar statements are proved also if an additional information
on a signal smoothness is given.
By theorems on asymptotic equivalence of statistical experiments
these results are extended to the problems of testing nonparametric
hypotheses
on density and regression. The exact asymptotically minimax
lower bounds of type II error probabilities are pointed out for
all these settings. Similar results are also obtained for the problems
of testing parametric hypotheses versus nonparametric sets of alternatives.

LA - eng

KW - Nonparametric hypothesis testing;
kernel-based tests; goodness-of-fit tests; efficiency; asymptotic minimaxity;
kernel estimator.; kernel-based tests; kernel estimators

UR - http://eudml.org/doc/104309

ER -

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