Computerized obstructive sleep apnea detection is necessary to speed-up sleep apnea diagnosis and research and for assisting medical professionals. Moreover, the development of a device to monitor sleep apnea that is low-power and portable, requires a reliable and successful sleep apnea detection scheme. In this article, the problem of automated sleep apnea detection using singe-lead electrocardiogram (ECG) signals has been addressed. At first, segments of ECG signals are decomposed using a data-adaptive signal decomposition scheme, namely- tunable-Q factor wavelet transform (TQWT). Three statistical features are extracted from the TQWT sub-bands and train and test matrices are formed afterwards. These matrices are fed into the classifier to identify non-apneic and apneic ECG signal segments. In this work, a new machine learning algorithm, namely random under sampling boosting (RUSBoost) is implemented to perform classification. This is for the first time TQWT along with RUSBoost is employed for automatic sleep apnea detection to our knowledge. The overall algorithmic performance of our method is inspected for various values of TQWT parameters. Optimal values of these parameters are investigated and determined. The efficacy and appropriateness of RUSBoost are demonstrated as opposed to the commonly used classification models. The algorithmic performance of our sleep apnea identification scheme is also evaluated against existing detection algorithms in the literature. Experimental outcomes manifest that our sleep apnea identification scheme performs better than the existing works in sensitivity, specificity, and accuracy. It can be anticipated that owing to its use of only one channel of ECG signal, the proposed method will be ideal for device implementation, eliminate the onus of clinicians of analyzing a large bulk of data manually, and expedite sleep apnea diagnosis.