1. A method for automatic detection of sleep apnea implemented in a medical apparatus; said method comprising: (a) extracting a plurality of signal features by analyzing an oxygen saturation signal; (b) performing dimensionality reduction based on principal component analysis (PCA) on said plurality of signal features to generate a plurality of signal features in a transformed space, wherein said plurality of signal features comprise (1) a plurality of power spectral density metrics including computing a total area under the power spectral density, computing an area over a user-specified frequency band, and computing a peak amplitude over said user-specified frequency band; and (2) a plurality of nonlinear analysis metrics including approximate entropy (ApEn), a central tendency measure (CTM), and Lempel-Ziv complexity (LZC); and (c) reporting a sleep apnea diagnosis result based on a statistical classifier that operates on said plurality of signal features in said transformed space.