Detecting early signs of neurodegeneration is vital for planning treatments for neurological diseases. Speech plays an important role in this context because it has been shown to be a promising early indicator of neurological decline, and because it can be acquired remotely without the need for specialized hardware. Typically, symptoms are characterized by clinicians using subjective and discrete scales. The poor resolution and subjectivity of these scales can make the earliest speech changes hard to detect. In this paper, we propose an algorithm for the objective assessment of vocal tremor, a phenomenon associated with many neurological disorders. The algorithm extracts and aggregates a feature set from the average spectra of the energy and fundamental frequency profiles of a sustained phonation. We show that the resultant low-dimensional feature set reliably classifies healthy controls and patients with amyotrophic lateral sclerosis perceptually rated for tremor by speech language pathologists.