A semi-parametric test based on a quasi-likelihood approach for comparing the estimated spectra of two neural spike trains

In this work, we provide a semi-parametric approach for testing the hypothesis that the spectra of two neural spike trains are equal. Estimates of the spectra are obtained by taking the Fourier transforms of the cumulant functions using convergence factors for smoothing. A quasi-likelihood ratio test for comparing different hypotheses is applied since the estimates are asymptotically Normal with constant variances. An illustrative example is presented where the information transferred to the spinal cord from the muscle spindle, under the influence of two stimuli can be separated into two parts 0–19 and 19–120 Hz. The dependence on the frequency in both parts is of a quadratic form.