Sleep deficiency impacts the quality of life and may have serious health consequences in the long run. Questionnaire-based subjective assessment of sleep deficiency has many limitations. On the other hand, objective assessment of sleep deficiency is challenging. In this study, we propose a polysomnography-based mathematical model for computing baseline sleep deficiency severity score and then investigated the estimation of sleep deficiency severity using features available only from wearable sensor data including heart rate variability and single-channel electroen-cephalography for a dataset of 500 subjects. We used Monte-Carlo Feature Selection (MCFS) and inter-dependency discovery for selecting the best features and removing multi-collinearity. For developing the Regression model we investigated both the frequentist and the Bayesian ap-proaches. An Artificial Neural Network achieved the best performance of RMSE = 5.47 and an R-squared value of 0.67 for sleep deficiency severity estimation. The developed method is com-parable to conventional methods of Functional Outcome of Sleep Questionnaire and Epworth Sleepiness Scale for assessing the impact of sleep apnea on sleep deficiency. Moreover, the results pave the way for reliable and interpretable sleep deficiency severity estimation using a wearable device in Smart Health.