25,928 research outputs found
Optimal Calibration for Multiple Testing against Local Inhomogeneity in Higher Dimension
Based on two independent samples X_1,...,X_m and X_{m+1},...,X_n drawn from
multivariate distributions with unknown Lebesgue densities p and q
respectively, we propose an exact multiple test in order to identify
simultaneously regions of significant deviations between p and q. The
construction is built from randomized nearest-neighbor statistics. It does not
require any preliminary information about the multivariate densities such as
compact support, strict positivity or smoothness and shape properties. The
properly adjusted multiple testing procedure is shown to be sharp-optimal for
typical arrangements of the observation values which appear with probability
close to one. The proof relies on a new coupling Bernstein type exponential
inequality, reflecting the non-subgaussian tail behavior of a combinatorial
process. For power investigation of the proposed method a reparametrized
minimax set-up is introduced, reducing the composite hypothesis "p=q" to a
simple one with the multivariate mixed density (m/n)p+(1-m/n)q as infinite
dimensional nuisance parameter. Within this framework, the test is shown to be
spatially and sharply asymptotically adaptive with respect to uniform loss on
isotropic H\"older classes. The exact minimax risk asymptotics are obtained in
terms of solutions of the optimal recovery
Adaptive goodness-of-fit tests based on signed ranks
Within the nonparametric regression model with unknown regression function
and independent, symmetric errors, a new multiscale signed rank statistic
is introduced and a conditional multiple test of the simple hypothesis
against a nonparametric alternative is proposed. This test is distribution-free
and exact for finite samples even in the heteroscedastic case. It adapts in a
certain sense to the unknown smoothness of the regression function under the
alternative, and it is uniformly consistent against alternatives whose sup-norm
tends to zero at the fastest possible rate. The test is shown to be
asymptotically optimal in two senses: It is rate-optimal adaptive against
H\"{o}lder classes. Furthermore, its relative asymptotic efficiency with
respect to an asymptotically minimax optimal test under sup-norm loss is close
to 1 in case of homoscedastic Gaussian errors within a broad range of
H\"{o}lder classes simultaneously.Comment: Published in at http://dx.doi.org/10.1214/009053607000000992 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Cognitive-Behavioral Treatment for Depression in Adolescents
The goal of this article is to briefly review and summarize the rationale and research support for cognitivebehavioral
therapy (CBT) as a treatment for depressed adolescents. A primary focus of the paper is on our
group CBT treatment for adolescent depression, entitled “The Adolescent Coping with Depression Course”.
In addition, initial findings from a large, recently-completed study contrasting individual CBT with
fluoxetine for depressed adolescents (Treatment of Adolescents with Depression Study) are presented.
Although the research support for CBT as a treatment for depressed adolescents is generally encouraging,
we need to better understand which depressed adolescents benefit from CBT, how and when to incorporate
medication and family-based interventions into CBT treatment, how to treat depressed adolescents with comorbid
psychiatric conditions, and how CBT interventions fare with non-European-American depressed
adolescents
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