Snoring is the most common symptom of obstructive sleep apnea hypopnea syndrome (OSAHS), which is a serious disease with high community prevalence. The standard method of OSAHS diagnosis, known as polysomnography (PSG), is expensive and time consuming. There is evidence suggesting that snore-related sounds (SRS) carry sufficient information to diagnose OSAHS. In this paper we present a technique for diagnosing OSAHS based solely on snore sound analysis. The method comprises a logistic regression model fed with snore parameters derived from its features such as the pitch and total airway response (TAR) estimated using a higher order statistics (HOS)-based algorithm. Pitch represents a time domain characteristic of the airway vibrations and the TAR represents the acoustical changes brought about by the collapsing upper airways. The performance of the proposed method was evaluated using the technique of K-fold cross validation, on a clinical database consisting of overnight snoring sounds of 41 subjects. The method achieved 89.3% sensitivity with 92.3% specificity (the area under the ROC curve was 0.96). These results establish the feasibility of developing a snore-based OSAHS community-screening device, which does not require any contact measurements.