Estimating the Number of Signals in Mixed Data with Stationary Colored Noise in the Absence of Reference Noise Samples

• Activity Number: 86
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: International Indian Statistical Association
• Author(s): Rajesh Nandy*+
• Keywords: Independent Component Analysis ; Dimension estimation ; Correlated noise ; MDL ; BIC ; PCA

Abstract

The estimation of number of signals in noisy data is a problem of interest. There exists an extensive body of work to address this specific problem primarily using the eigenspectrum of the data covariance matrix. There are two popular approaches to the analysis on the eigenspectrum. The first approach uses information theoretic criteria such as AIC, MDL and BIC, whereas the second approach uses statistical hypothesis testing utilizing the distributional properties of the noise covariance. Each of these methods assumes one of the following; the noise is white, the noise covariance is known, there is a reference noise sample to estimate the noise covariance matrix or the noise covariance has a very specific form. A novel method using independent component analysis (ICA) is presented to estimate the number of signals in mixed data under the weak assumption of stationarity for the noise. The final estimation is performed using MDL, but the method is versatile enough to be implemented in conjunction with other approaches. Results from the proposed approach are compared with results in the presence of noise-only sample and also with results from MDL when no adjustment is performed.