25 research outputs found
A simple forward selection procedure based on false discovery rate control
We propose the use of a new false discovery rate (FDR) controlling procedure
as a model selection penalized method, and compare its performance to that of
other penalized methods over a wide range of realistic settings: nonorthogonal
design matrices, moderate and large pool of explanatory variables, and both
sparse and nonsparse models, in the sense that they may include a small and
large fraction of the potential variables (and even all). The comparison is
done by a comprehensive simulation study, using a quantitative framework for
performance comparisons in the form of empirical minimaxity relative to a
"random oracle": the oracle model selection performance on data dependent
forward selected family of potential models. We show that FDR based procedures
have good performance, and in particular the newly proposed method, emerges as
having empirical minimax performance. Interestingly, using FDR level of 0.05 is
a global best.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS194 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Peak Detection as Multiple Testing
This paper considers the problem of detecting equal-shaped non-overlapping
unimodal peaks in the presence of Gaussian ergodic stationary noise, where the
number, location and heights of the peaks are unknown. A multiple testing
approach is proposed in which, after kernel smoothing, the presence of a peak
is tested at each observed local maximum. The procedure provides strong control
of the family wise error rate and the false discovery rate asymptotically as
both the signal-to-noise ratio (SNR) and the search space get large, where the
search space may grow exponentially as a function of SNR. Simulations assuming
a Gaussian peak shape and a Gaussian autocorrelation function show that desired
error levels are achieved for relatively low SNR and are robust to partial peak
overlap. Simulations also show that detection power is maximized when the
smoothing bandwidth is close to the bandwidth of the signal peaks, akin to the
well-known matched filter theorem in signal processing. The procedure is
illustrated in an analysis of electrical recordings of neuronal cell activity.Comment: 37 pages, 8 figure
Multiple testing of local maxima for detection of peaks in 1D
A topological multiple testing scheme for one-dimensional domains is proposed
where, rather than testing every spatial or temporal location for the presence
of a signal, tests are performed only at the local maxima of the smoothed
observed sequence. Assuming unimodal true peaks with finite support and
Gaussian stationary ergodic noise, it is shown that the algorithm with
Bonferroni or Benjamini--Hochberg correction provides asymptotic strong control
of the family wise error rate and false discovery rate, and is power
consistent, as the search space and the signal strength get large, where the
search space may grow exponentially faster than the signal strength.
Simulations show that error levels are maintained for nonasymptotic conditions,
and that power is maximized when the smoothing kernel is close in shape and
bandwidth to the signal peaks, akin to the matched filter theorem in signal
processing. The methods are illustrated in an analysis of electrical recordings
of neuronal cell activity.Comment: Published in at http://dx.doi.org/10.1214/11-AOS943 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
An adaptive step-down procedure with proven FDR control under independence
In this work we study an adaptive step-down procedure for testing
hypotheses. It stems from the repeated use of the false discovery rate
controlling the linear step-up procedure (sometimes called BH), and makes use
of the critical constants , . Motivated by its
success as a model selection procedure, as well as by its asymptotic
optimality, we are interested in its false discovery rate (FDR) controlling
properties for a finite number of hypotheses. We prove this step-down procedure
controls the FDR at level for independent test statistics. We then
numerically compare it with two other procedures with proven FDR control under
independence, both in terms of power under independence and FDR control under
positive dependence.Comment: Published in at http://dx.doi.org/10.1214/07-AOS586 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Дерматофибросаркома: обзор литературы и клиническое наблюдение
Among the cases with malignant tumor we have only 0,01% of patients diagnosed with dermatofibrosarcoma, and 2-6% affected with soft tissue tumor. This article deals with the morphological peculiarities of this tumor, character of disease progression, the criteria and complexity of diagnosis, and the tactics of treatment, as well as the estimation of the long-term treatment results. We consider a clinical case of a man (37 years old) diagnosed with the recurrence of soft tissue tumor which shows the complexity of diagnosis and treatment of this disease.Дерматофибросаркома встречается в 0,01% случаев среди всех злокачественных опухолей и 2-6% среди опухолей мягких тканей. В статье представлены морфологические особенности данной опухоли, характер течения заболевания, критерии и сложности диагностики и тактика лечения, а также прогноз отдаленных результатов. Приведено клиническое наблюдение рецидивирующей опухоли мягких тканей у мужчины 37 лет, иллюстрирующее сложности диагностики и лечения данной патологии