FDR control of detected regions by multiscale matched filtering

ABSTRACT

Feature extraction from observed noisy samples is a common important problem in statistics and engineering. This paper presents a novel general statistical approach to the region detection problem in long data sequences. The proposed technique is a multiscale kernel regression in conjunction with statistical multiple testing for region detection while controlling the false discovery rate (FDR) and maximizing the signal-to-noise ratio via matched filtering. This is achieved by considering a one-dimensional region detection problem as its equivalent zero-dimensional peak detection problem. The detection method does not require a priori knowledge of the shape of the nonzero regions. However, if the shape of the nonzero regions is known a priori, e.g., rectangular pulse, the signal regions can also be reconstructed from the detected peaks, seen as their topological point representatives. Simulations show that the method can effectively perform signal detection and reconstruction in the simulated data under high noise conditions, while controlling the FDR of detected regions and their reconstructed length.

Keywords:

• FDR control
• Matched filtering
• Multiscale bandwidth
• Kernel regression
• Region detection

Mathematics Subject Classification:

• 62G08

Acknowledgments

The authors would like to thank Dr. Yen-Tsun Huang from Brown University and Prof. Giovanni Parmigiani from DFCI for discussions about DNA copy number data of lung cancer.

Funding

The authors also thank NIH for supporting this research through Grant P01 CA134294-03.