Multiple Testing of Local Extrema for Detection of Change Points

A new approach to change point detection based on smoothing and multiple testing is presented for long data sequences modeled as piecewise constant functions plus stationary ergodic Gaussian noise. As an application of the STEM algorithm for peak detection developed in \citet{Schwartzman:2011} and \citet{CS:2014b}, the method detects change points as significant local maxima and minima after smoothing and differentiating the observed sequence. The algorithm, combined with the Benjamini-Hochberg procedure for thresholding p-values, provides asymptotic strong control of the False Discovery Rate (FDR) and power consistency, as the length of the sequence and the size of the jumps get large. Simulations show that FDR levels are maintained in non-asymptotic conditions and guide the choice of smoothing bandwidth with respect to the desired location tolerance. The methods are illustrated in genomic array-CGH data.